Abiraterone Acetate and Prednisone With or Without Dasatinib in Treating Patients With Metastatic Hormone-Resistant Prostate Cancer

Inclusion Criteria: * Metastatic, castration-resistant prostate cancer * Defined as evaluable radiographic disease with rising PSA x 2 (at least 1 week apart) or radiographic progression (new soft tissue/bone lesions or enlarging soft tissue lesions) despite medical or surgical castration * No limit on prior hormonal therapies (i.e. anti-androgens, ketoconazole) except that subject must not have received abiraterone previously * No limit on prior biologic therapies (i.e. immune therapy, antiangiogenic, targeted) except that patient should not have received dasatinib or other v-src sarcoma (Schmidt-Ruppin A-2) viral oncogene homolog (avian) (src)-targeted therapy * No prior chemotherapy for metastatic disease \* Subjects who have received chemotherapy in the neoadjuvant or adjuvant setting will be eligible provided chemotherapy was completed \> 6 months prior to enrollment * Eastern Cooperative Oncology Group (ECOG) 0-2 * Total bilirubin =\< 1.5 times the institutional upper limit of normal (ULN) except for Gilbert's syndrome * Hepatic enzymes (aspartate aminotransferase \[AST\], alanine aminotransferase \[ALT\] ) =\< 2.5 times the institutional ULN * Serum sodium (Na), potassium (K+), magnesium (Mg+), phosphate and calcium (Ca+) \> lower limit of normal (LLN) * Serum creatinine =\< 1.5 time the institutional ULN * Hemoglobin (Hb) \>= 9 * Platelets \>= 100,000 * Absolute neutrophil count (ANC) \>= 1000 * Ability to take oral medication (study medications must be swallowed whole) * Men with fathering potential must agree to use contraception throughout study treatment; acceptable methods include: condoms, sponge, intrauterine device (IUD), oral contraceptives * Concomitant medications \* Patient agrees to discontinue St. Johns wort while receiving dasatinib therapy (discontinue St. Johns wort at least 5 days before starting dasatinib) Exclusion Criteria: * Known hepatitis B or C or human immunodeficiency virus (HIV), regardless of viral load \* Testing for the purposes of enrollment is not mandatory, however a documented history of these infections will be exclusionary due to concerns for drug-drug interactions with antivirals and potential for increased risk of liver toxicity * Radiation for palliation of bony metastases within the preceding 2 weeks * Prior chemotherapy for metastatic castration-resistant prostate cancer (CRPC) \* Immune therapy with sipuleucel-T is allowed, provided the last infusion was \>= 28 days prior to study therapy and there has been at least one documented PSA value rising after completion of sipuleucel-T therapy or progression of disease on imaging after sipuleucel-T * Malignancy (aside from prostate cancer) which required radiotherapy or systemic treatment within the past 5 years * Superficial bladder cancer treated with intravesical therapy and currently in remission will not be an exclusion * Skin cancers will not be an exclusion, except for melanoma with a thickness \> 1 mm * Concurrent medical condition which may increase the risk of toxicity, including: * Pleural or pericardial effusion of any grade at the time of study entry * Cardiac symptoms; any of the following should be considered for exclusion: \*\* Uncontrolled angina, congestive heart failure or myocardial infarction (MI) within (6 months) * Diagnosed congenital long QT syndrome * Any history of clinically significant ventricular arrhythmias (such as ventricular tachycardia, ventricular fibrillation, or Torsades de pointes) \*\* Prolonged QTc/f interval on pre-entry electrocardiogram (\> 450 msec) * Hypokalemia or hypomagnesemia if it cannot be corrected prior to abiraterone administration * History of significant bleeding disorder unrelated to cancer, including: * Diagnosed congenital bleeding disorders (e.g., von Willebrand's disease) * Diagnosed acquired bleeding disorder within one year (e.g., acquired anti-factor VIII antibodies) * Ongoing or recent (=\< 3 months) significant gastrointestinal bleeding * Prohibited treatments and/or therapies * Should not be on any additional anti-cancer therapy except for luteinizing hormone-releasing hormone (LHRH) agonist/antagonist; specifically excluded medications include ketoconazole, estrogens, and anti-androgens * Category I drugs that are generally accepted to have a risk of causing Torsades de pointes including: (Patients must discontinue drug 7 days prior to starting dasatinib) * Quinidine, procainamide, disopyramide * Amiodarone, sotalol, ibutilide, dofetilide * Erythromycin, clarithromycin * Chlorpromazine, haloperidol, mesoridazine, thioridazine, pimozide * Cisapride, bepridil, droperidol, methadone, arsenic, chloroquine, domperidone, halofantrine, levomethadyl, pentamidine, sparfloxacin, lidoflazine * Prisoners or subjects who are involuntarily incarcerated * Subjects who are compulsorily detained for treatment of either a psychiatric or physical (eg, infectious disease) illness