Carboplatin, Paclitaxel, Bevacizumab, and Veliparib in Treating Patients With Newly Diagnosed Stage II-IV Ovarian Epithelial, Fallopian Tube, or Primary Peritoneal Cancer

Inclusion Criteria: * Patients with a histologic diagnosis of epithelial ovarian, fallopian tube, or primary peritoneal carcinoma, or carcinosarcoma stage II, III, or IV with either optimal (=\< 1 cm residual disease) or suboptimal residual disease * All patients must have a procedure for determining diagnosis of epithelial ovarian, fallopian tube, primary peritoneal, or carcinosarcoma with appropriate tissue for histologic evaluation * Patients with the following histologic cell types are eligible: * Serous adenocarcinoma, endometrioid adenocarcinoma, mucinous adenocarcinoma, undifferentiated carcinoma, clear cell adenocarcinoma, mixed epithelial adenocarcinoma, transitional cell carcinoma, malignant Brenner's tumor, adenocarcinoma not otherwise specified (N.O.S.) or carcinosarcoma * Absolute neutrophil count (ANC) greater than or equal to 1,500/mm\^3, equivalent to CTEP Common Terminology Criteria for Adverse Events (CTCAE) version 4.0, grade 1; this ANC cannot have been induced or supported by granulocyte colony stimulating factors * Platelets greater than or equal to 100,000/mm\^3 * Regimens I and II: Creatinine =\< 1.5 x institutional upper limit normal (ULN), CTCAE grade 1 * Regimen III: Creatinine no greater than the institutional upper limits of normal * Bilirubin less than or equal to 1.5 x ULN (CTEP CTCAE version 4.0, grade 1) * Serum glutamic oxaloacetic transaminase (SGOT) (aspartate aminotransferase \[AST\]) less than or equal to 3 x ULN (CTEP CTCAE versio…