Testing Two Oral Drugs Combination (Cediranib and Olaparib) Compared to a Single Drug (Olaparib) for Men With Advanced Prostate Cancer

Inclusion Criteria: * Patients must have histologically confirmed progressive, metastatic castration resistant prostate adenocarcinoma by meeting ALL the following: * Pathology of prostate gland or metastatic disease must confirm the diagnosis of prostate adenocarcinoma; mixed histology with other variants including but not limited to small cell or neuroendocrine differentiation must be discussed with the study principal investigator (PI) * Metastasis must be documented by radiographic evidence * Castration resistance must be documented with surgical or medical castration with serum testosterone \< 50 ng/dL (\< 2.0 nM); if the patient is being treated with luteinizing hormone-releasing hormone (LHRH) agonists (patient who has not undergone orchiectomy), this therapy must have been initiated at least 4 weeks prior to cycle 1, day 1 and must be continued throughout the study * Progression must be evidenced and documented by any of the following parameters * Two consecutively rising PSA values, above the baseline, at a minimum of 1-week intervals; the minimal value to enter the study is 1.0 ng/ml or greater; the reference value (#1) is the last PSA measured before increases are documented, with subsequent values obtained a minimum of 1 week apart; if the PSA at time point 3 (value #3A) is greater than that at point 2, then eligibility has been met; if the PSA is not greater than point 2 (value #3B), but value #4 is, the patient is eligible assuming that other criteria are met, if values 3A or #4 are 1 ng/mL or higher (Prostate Cancer Working Group 3) * Appearance of one or more new lesions on bone scan * Progressive disease by RECIST 1.1 * Must have a tumor lesion safely accessible for biopsy per the investigator's discretion; while a soft tissue metastasis is preferred for a biopsy, a bone metastasis is allowed for biopsy as long as enough cores can be obtained; a biopsied lesion cannot be used for target lesion for response assessment * Must be agreeable to the mandatory research tumor biopsies (pre-treatment and on-treatment); tumor biopsies are mandatory at pre-treatment and at on-treatment; there is an optional biopsy at post-progression * Must have received at least one prior line of therapy for mCRPC; a taxane chemotherapy administered for metastatic castration sensitive disease will not count, unless patient develops disease progression within 12 months from the last dose chemotherapy * Must have a life expectancy greater than or equal to 16 weeks * If patient is currently on prednisone or other corticosteroids for palliation, the dose must be less than or equal to 10 mg a day or its equivalent dose and it must have been started at least 4 weeks prior to cycle 1 day 1 * Patients must have measurable disease by RECIST v1.1, or evaluable disease with bone metastases demonstrated by Tc99 bone scan; patients with bone metastases only are allowed (NOTE: nodes \>= 1.5 cm (not \>= 2 cm) in the short axis are considered measurable, per The Prostate Cancer Working Group 3 \[PCWG3\]) * Toxicities of prior therapy (except alopecia) should be resolved to =\< grade 1 as per National Cancer Institute-Common Terminology Criteria for Adverse Events (NCI-CTCAE) v5.0; patients with long-standing stable grade 2 neuropathy or others (e.g., adrenal insufficiency or hypothyroidism on stable doses of replacement therapy) may be allowed after discussion with the study principal investigator (PI) * Age \>= 18 years. There is no dosing or adverse event data currently available on the use of cediranib or olaparib in patients \< 18 years of age, thus excluding them from enrollment * Eastern Cooperative Oncology Group (ECOG) performance status 0 or 1 (Karnofsky \>= 70%) * White blood count (WBC) \> 3 x 10\^9/L (within 28 days prior to administration of study treatment) * Absolute neutrophil count \>= 1,500/mcL (within 28 days prior to administration of study treatment) * Platelets \>= 100,000/mcL (within 28 days prior to administration of study treatment) * Hemoglobin \>= 10 g/dL with no pack red blood cell transfusion in the past 28 days (within 28 days prior to administration of study treatment) * Creatinine clearance \>= 51 mL/min, calculated using Cockcroft-Gault formula (within 28 days prior to administration of study treatment) * Urine protein: creatinine ratio (UPC) of =\< 1 (within 28 days prior to administration of study treatment) * Total bilirubin =\< 1.5 x the institutional upper limit of normal (ULN) (within 28 days prior to administration of study treatment) * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamic pyruvic transaminase \[SGPT\]) \< 3 times institutional ULN unless liver metastases are present in which case they must be \< 5 x ULN (within 28 days prior to administration of study treatment) * Coagulation parameters (international normalized ratio \[INR\] and activated partial thromboplastin time \[aPTT\]) within 1.25 x ULN institutional limits, except where a lupus anti-coagulant has been confirmed, or except patients on anticoagulation (within 28 days prior to administration of study treatment) * Patients must be able to swallow oral medications and not have gastrointestinal illnesses that would preclude absorption of cediranib or olaparib * Adequately controlled thyroid function, with no symptoms of thyroid dysfunction; patients can be on thyroid hormone replacement medication; asymptomatic patients with elevated thyroid-stimulating hormone (TSH) with normal T4/T3 are allowed to enroll, and recommended to follow with routine thyroid function test especially if they are randomized to cediranib/olaparib arm * Adequately controlled blood pressure (BP) \< 140 mmHg (systolic) and \< 90 mmHg (diastolic) taken in the clinic setting by a medical professional within 2 weeks prior to starting study; patients with hypertension may be managed with up to a maximum of 3 antihypertensive medications; patients who are on 3 antihypertensive medications are highly recommended to be followed by a cardiologist or blood pressure specialist for management of BP while on protocol * Patients must be willing and able to check and record daily blood pressure readings when randomized to cediranib containing arm * Patients must have documented left ventricular ejection fraction (LVEF) by echocardiogram greater than institution's lower limit of normal (or 55% if threshold for normal not otherwise specified by institutional guidelines) obtained within 3 months prior to registration if they have any of the following risk factors for cardiac toxicities: * A New York Heart Association (NYHA) classification of II controlled with treatment * Prior central thoracic radiation therapy (RT), including RT to the heart * History of myocardial infarction within 12 months prior to registration * Prior treatment with anthracyclines * Prior treatment with trastuzumab * Prior history of other significant impaired cardiac function * Male participants and their female partners, who are sexually active and of childbearing potential, must agree to the use of two highly effective forms of contraception in combination (see below for acceptable methods), and not to donate sperm, throughout the period of taking study treatment and for 3 months after last dose of study drug(s) to prevent pregnancy in a partner; acceptable methods of contraception to be used in this study include: * Condom with spermicide and one of the following: * Oral contraceptive or hormonal therapy (e.g. hormone implants) * Placement of an intra-uterine device * Acceptable non-hormonal birth control methods include: * Total sexual abstinence; abstinence must be for the total duration of the study and the drug washout period * Vasectomized sexual partner plus male condom; with participant assurance that partner received post-vasectomy confirmation of azoospermia * Tubal occlusion plus male condom with spermicide * Intrauterine device (IUD) plus male condom+spermicide; provided coils are copper-banded * Acceptable hormonal methods: * Etonogestrel implants (e.g., Implanon, Norplan) + male condom with spermicide * Normal and low dose combined oral pills + male condom with spermicide * Norelgestromin/ethinyl estradiol (EE) transdermal system + male condom with spermicide * Intravaginal device + male condom with spermicide (e.g., EE and etonogestrel) * Cerazette (desogestrel) + male condom with spermicide; cerazette is currently the only highly efficacious progesterone based pill * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy, hormonal therapy (except LHRH agonist or antagonist), immunotherapy, radioisotope therapy, or RT within 21 days prior to start of the study agents * Initiating bisphosphonate, or RANKL antibody therapy or adjusting the dose/regimen within 30 days prior to cycle 1 day 1 is prohibited; patients on a stable bisphosphonate regimen are eligible and may continue * Patients who have received any other investigational agents within the past 28 days prior to cycle 1 day 1 * Patients with untreated brain metastases, spinal cord compression, or evidence of symptomatic brain metastases or leptomeningeal disease as noted on computed tomography (CT) or magnetic resonance imaging (MRI) scans are excluded from this clinical trial; while screening brain MRI is not required, it should be performed if clinically indicated at the discretion of the treating investigator; should patient found to have brain metastasis, treatment of brain metastasis must precede the participation in this study * For patients with known and treated brain metastases is allowed in this study if they fulfill ALL of the following criteria: * The lesions have remained radiologically stable for at least six weeks after completion of brain irradiation or stereotactic brain radiosurgery, and must remain stable at the time of study entry * There is no mass effect present radiologically and no steroids requirement for symptom control for more than 4 weeks * Patients who have received a prior inhibitor of vascular endothelial growth factor (VEGF) signaling inhibitor, or a poly adenosine diphosphate-ribose polymerase (PARP) inhibitor administered * History of allergic reactions attributed to compounds of similar chemical or biologic composition to cediranib or olaparib * Concomitant use of known strong CYP3A inhibitors (e.g. itraconazole, telithromycin, clarithromycin, protease inhibitors boosted with ritonavir or cobicistat, indinavir, saquinavir, nelfinavir, boceprevir, telaprevir), moderate CYP3A inhibitors (e.g. ciprofloxacin, erythromycin, diltiazem, fluconazole, verapamil), strong CYP3A inducers (e.g. phenobarbital, enzalutamide, phenytoin, rifampicin, rifabutin, rifapentine, carbamazepine, nevirapine and St John's wort) or moderate CYP3A inducers (e.g. bosentan, efavirenz, modafinil); a minimum washout period of 2 weeks prior to cycle 1 day 1 is required for strong inhibitors, and at least one week for moderate inhibitors; a minimum washout period of 4 weeks prior to cycle 1 day 1 is required for CYP3A inducers; a minimum washout period of 5 weeks prior to cycle 1 day 1 is required for enzalutamide or phenobarbital; dihydropyridine calcium-channel blockers are permitted for management of hypertension * Current use of natural herbal products or other "folk remedies"; if using previously, patients must stop using natural herbal products while participating in this study; multivitamin, calcium (Ca)/vitamin D (Vit D) and other vitamin complex supplements are allowed * Patients with concomitant or prior invasive malignancies within the past 5 years; subjects with limited stage basal cell or squamous cell carcinoma of the skin, carcinoma in situ of the breast, or non-muscle invasive bladder cancer, are eligible as long as they received curative intent therapy * Uncontrolled intercurrent illness including, but not limited to, uncontrolled seizures ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Resting ECG with corrected QT (QTc) \> 470 msec on two or more time points within a 24 hour period, noted within 14 days of treatment, or family history of long QT syndrome * History of myocardial infarction within 6 months of the randomization * History of stroke or transient ischemic attack within 6 months of the randomization * NYHA classification of III or IV * Current cardiac arrhythmic condition requiring concurrent use of anti-arrhythmic drug; rate controlled atrial fibrillation is allows * History of hypertensive crisis or hypertensive encephalopathy within 3 years of the randomization * Clinically significant peripheral vascular disease or known abdominal aortic aneurysm ( \> 5 cm in diameter) or history of aortic dissection; patients with known history of abdominal aortic aneurysm (AAA) with \>= 4 cm in diameter, a repeat ultrasound (US) within the last 6 months prior to randomization will be required to document that it is =\< 5 cm, and patient must be asymptomatic from the aneurysm, and the blood pressure must be well controlled as required in this protocol * A major surgical procedure, open biopsy, or significant traumatic injury within 3 months prior to cycle 1 day 1 (percutaneous/endobronchial/endoscopic biopsies are allowed) * History of bowel obstruction within 1 month prior to starting study drugs * History of hemoptysis within the last 1 month prior to randomization * Presence of cavitation of central pulmonary lesion, or radiographic evidence of pneumonitis or other extensive bilateral lung disease such as interstitial lung disease * Any history of gastrointestinal (GI) perforation, history of intra-abdominal abscess within 3 months prior to starting treatment, or history of abdominal fistula unless the fistula history meets all the following: (a) the fistula was surgically repaired, (b) there has been no evidence of fistula for at least 6 months prior to starting treatment, (c) patient is deemed to be at low risk of recurrent fistula, and (d) the case must be discussed with the study PI * Current dependency on intravenous (IV) hydration or total parenteral nutrition (TPN) * Known coagulopathy or bleeding diathesis; those on therapeutic anticoagulation or anti-platelet agent are permitted only after discussing with the study PI * Patients with history of intra-abdominal bleeding or retroperitoneal bleeding within the last 3 years are excluded * Patients with myelodysplastic syndrome (MDS) or acute myelogenous leukemia (AML), or features suggestive of MDS/AML * Patients with known active human immunodeficiency virus (HIV), hepatitis B or hepatitis C infection; it is because of the potential requirement for anti-viral therapies that are prohibited on the study; patients with a history of hepatitis B or hepatitis C, who are deemed cured and no longer require treatment may be allowed to enroll after consultation with the respective specialist and the study PI * Previous allogenic bone marrow transplant or double umbilical cord blood transplantation (dUCBT) * Whole blood transfusions in the last 120 days prior to entry to the study * Involvement in the planning and/or conduct of the study (applies to both AstraZeneca staff and/or staff at the study site) * Previous enrollment in the present study