A Phase II Neoadjuvant Study of Apalutamide, Abiraterone Acetate, Prednisone, Degarelix and Indomethacin in Men With Localized Prostate Cancer Pre-prostatectomy

Inclusion Criteria: * Willing and able to provide written informed consent * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Documented histologically confirmed adenocarcinoma of the prostate * Willing to undergo prostatectomy as primary treatment for localized prostate cancer * High risk prostate cancer (per National Comprehensive Cancer Network \[NCCN\] criteria): Gleason score 8-10 or T3a or PSA \> 20 ng/mL or very-high risk prostate cancer (per NCCN criteria): T3b-T4 * Serum testosterone \>= 150 ng/dL * Able to swallow the study drugs whole * Willing to take abiraterone acetate on an empty stomach (no food should be consumed at least two hours before and for one hour after dosing) * Agrees to use a condom (even men with vasectomies) and another effective method of birth control if he is having sex with a woman of childbearing potential or agrees to use a condom if he is having sex with a woman who is pregnant while on study drug and for 3 months following the last dose of study drug; must also agree not to donate sperm during the study and for 3 months after receiving the last dose of study drug * Medications known to lower the seizure threshold (see list under prohibited meds) must be discontinued or substituted at least 4 weeks prior to study entry Exclusion Criteria: * Prior local therapy to treat prostate cancer (e.g. radical prostatectomy, radiation therapy, brachytherapy) * Prior use of apalutamide, abiraterone acetate or degarelix * Prior or ongoing systemic therapy for prostate cancer including, but not limited to: * Hormonal therapy (for example \[e.g.\] leuprolide, goserelin, triptorelin, degarelix) * Cytochrome P450 (CYP)-17 inhibitors (e.g. ketoconazole) * Antiandrogens (e.g. bicalutamide, nilutamide) * Second generation antiandrogens (e.g. enzalutamide, apalutamide) * Immunotherapy (e.g. sipuleucel-T, ipilimumab) * Chemotherapy (e.g. docetaxel, cabazitaxel) * Evidence of serious and/or unstable pre-existing medical, psychiatric or other condition (including laboratory abnormalities) that could interfere with patient safety or provision of informed consent to participate in this study * Any psychological, familial, sociological, or geographical condition that could potentially interfere with compliance with the study protocol and follow-up schedule * Absolute neutrophil count \[ANC\] \< 1500/mm\^3 * Platelet count \< 100,000/mm\^3 * Hemoglobin \< 9 g/dL * Total bilirubin \> 1.5 x upper limit of normal (ULN) * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \>= 2.5 x ULN; Note: in subjects with Gilbert's syndrome, if total bilirubin is \> 1.5 x ULN, measure direct and indirect bilirubin and if direct bilirubin is =\< 1.5 x ULN, subject may be eligible * Abnormal kidney function (glomerular filtration rate GFR \< 45 mL/min) * Serum albumin \< 3 g/dL * Serum potassium \< 3.5 mmol/L * Seizure or known condition that may pre-dispose to seizure (e.g. prior stroke within 1 year to randomization, brain arteriovenous malformation, schwannoma, meningioma, or other benign central nervous system \[CNS\] or meningeal disease which may require treatment with surgery or radiation therapy) * Severe or unstable angina, myocardial infarction, symptomatic congestive heart failure, arterial or venous thromboembolic events (eg, pulmonary embolism, cerebrovascular accident including transient ischemic attacks), or clinically significant ventricular arrhythmias within 6 months prior to randomization * History of stroke within the last 5-years * History of gastrointestinal (GI) bleed requiring transfusion * History of peptic ulcer disease requiring treatment within the last 5-years * History of asthma that is nonsteroidal anti-inflammatory drug (NSAID)-induced or with asthma that is classified as 'mild-persistent' or worse (based on symptoms occurring more than 2 days per week) * Uncontrolled hypertension * Gastrointestinal disorder affecting absorption * Active infection (eg, human immunodeficiency virus \[HIV\] or viral hepatitis) * Any chronic medical condition requiring a higher dose of corticosteroid than 10 mg prednisone/ prednisolone once daily * Any condition that in the opinion of the investigator, would preclude participation in this study * Child Pugh class B \& C * Pre-existing viral hepatitis