Aspirin and Rintatolimod With or Without Interferon-alpha 2b in Treating Patients With Prostate Cancer Before Surgery

Inclusion Criteria: * Histologically confirmed, localized prostate adenocarcinoma patients who are planning to have a radical prostatectomy. * Diagnostic prostate biopsy must have been obtained within 6 months patients who had biopsies at outside facilities may be eligible if tissue availability and adequacy can be confirmed by pathology. * Have an Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1. * Platelet \>= 75,000/uL. * Hemoglobin \>= 9 g/dL. * Hematocrit \>= 27%. * Absolute neutrophil count (ANC) \>= 1500/uL. * Creatinine \< institutional upper limit of normal (ULN) OR creatinine clearance \>= 50 mL/min for patients with creatinine levels greater than ULN. * Total bilirubin =\< 1.5 X institutional ULN. * Aspartate aminotransferase (AST) (serum glutamic oxaloacetic transaminase \[SGOT\]) and alanine aminotransferase (ALT) (serum glutamate pyruvate transaminase \[SGPT\]) =\< 1.5 X institutional ULN. * Serum amylase and lipase =\< 1.5 X institutional ULN. * Negative hepatitis panel for patients with a history of Hepatitis * Participant must understand the investigational nature of this study and sign an Independent Ethics Committee/Institutional Review Board approved written informed consent form prior to receiving any study related procedure. Exclusion Criteria: * Patients currently treated with systemic immunosuppressive agents, including steroids, are ineligible until 3 weeks after removal from immunosuppressive treatment. * Patients who received hormonal therapy, 5-alpha reductase inhibitors (such as finasteride, dutasteride), chemotherapy, radiotherapy, major surgery, or biologic therapy within 3 weeks of protocol treatment. * Patients with active prostatitis. * Patients with active autoimmune disease or history of transplantation. * Patients with comorbid medical conditions that render them unfit for surgery. * Metastatic disease based on preoperative imaging. * Cardiac risk factors including: * Patients experiencing cardiac event(s) (acute coronary syndrome, myocardial infarction, or ischemia) within 3 months of signing consent * Patients with a New York Heart Association classification of III or IV. * History of upper and lower gastrointestinal ulceration, upper gastrointestinal bleeding, or perforation within the past 3 years. * History of bleeding disorders, known lesions at risk for bleeding, or history of recent clinically significant bleed or hemorrhage (\<3months). * Prior allergic reaction or hypersensitivity to aspirin, or other nonsteroidal antiinflammatory drugs (NSAIDs). * Patients are ineligible if they plan on use of other NSAIDs at any dose during the trial. Patients who agree to stop regular NSAIDs are eligible and no wash out period is required. * Uncontrolled intercurrent illness including, but not limited to, 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. * Unwilling or unable to follow protocol requirements. * Any condition which in the investigator?s opinion deems the participant an unsuitable candidate to receive study drug.