Cediranib Maleate With or Without Dasatinib in Patients With HRPC-Resistant to Treatment With Docetaxel

Inclusion Criteria: * Histologically/cytologically confirmed prostate cancer * Measurable/non-measurable disease * Prior hormonal therapy with medical LHRH agonist or orchiectomy castration (Castrate level of testosterone (\< 50 ng/dL) required) * Clinical/radiographic evidence of progression on or after docetaxel therapy * No active pleural/pericardial effusion of any grade * No meningeal metastases/untreated known brain metastases * Patients with treated brain metastasis with radiologic, clinical evidence of stability, with no evidence of cavitation/hemorrhage in the brain lesions allowed if asymptomatic and not requiring corticosteroids * Life expectancy \>3 months * ECOG PS 0-2 (Karnofsky PS 60-100%) * ANC \>= 1,500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Hemoglobin \>= 9 g/dL * INR=\< 1.3 * Total bilirubin =\< 1.25 times ULN * AST and ALT=\< 2.0 times ULN (5 x ULN if clearly attributable to liver metastasis) * Creatinine normal OR creatinine clearance \>= 60 mL/min * LVEF\> institutional normal range by ECHO/MUGA * Urine dipstick for protein \< 1+ OR \< 1 g on 24-hour urine collection Exclusion Criteria: * \>5 years since any malignancy except in situ cancer, non-metastatic basal/squamous cell skin cancer, or other cancer for which the patient has been curatively treated * Fertile patients must use effective contraception * No condition that impairs ability to swallow/absorb * No history of allergic reactions attributed to compounds of similar chemical/biologic composition to cediranib/dasatinib * No systolic BP\>150 mmHg and/or diastolic BP\>100 mmHg * QTc prolongation (\>=480 msec by Fridericia correction) or other significant ECG abnormalities are ineligible * No active/uncontrolled infections, serious illness, or medical conditions that would not permit patient to be managed according to protocol * No known immunodeficiency syndrome * No clinical/radiological evidence of severe/uncontrolled interstitial lung disease * No history/concurrent idiopathic pulmonary fibrosis * No concurrent combination antiretroviral therapy for HIV-positive patients * No unresolved toxicity\>=CTCAE grade 2 (except alopecia) from prior anticancer therapy * 4 weeks since prior anti-androgens * 4 weeks since prior chemotherapy following docetaxel for metastatic disease (Any number of regimens allowed) * 4 weeks since prior hormonal therapy or abiraterone * 3 weeks since prior radioisotopes or radiotherapy and recovered * No prior therapy with angiogenesis or Src or FAK inhibitors * 3 weeks since prior major surgery and recovered * 1 week since prior corticosteroids * Concurrent zoledronic acid allowed provided patient has been receiving it prior to start of study treatment * Concurrent medications or substances known to affect or with the potential to affect the activity or pharmacokinetics of cediranib and dasatinib will be determined following review of their case by the principal investigator or co-investigator * 14 days before and after study and no concurrent CYP3A4-active agents or substances (including strong inhibitors or inducers) * Concurrent prophylactic low-dose warfarin (INR must be close monitored) or low-molecular weight heparin allowed * No other concurrent investigational agents