Vaccine Therapy and IDO1 Inhibitor INCB024360 in Treating Patients With Epithelial Ovarian, Fallopian Tube, or Primary Peritoneal Cancer Who Are in Remission

Inclusion Criteria: * Women with epithelial ovarian, fallopian tube, or primary peritoneal carcinoma and no evidence of disease or no measurable disease after 1st or 2nd line therapy; these patients would normally enter a period of observation after standard management * Any human leukocyte antigen (HLA) type; historic HLA typing is permitted * Tumor expression of NY-ESO-1 or cancer/testis antigen 2 (LAGE-1) by immunohistochemistry (IHC) and/or reverse transcription-polymerase chain reaction (RTPCR) * No allergy to eggs * Life expectancy \> 6 months * Hematology and biochemistry laboratory results within the limits normally expected for the patient population, without evidence of major organ failure * Absolute neutrophil count (ANC) \>= 1,000/uL * Platelet count (PLT) \>= 75,000/uL * Hemoglobin (Hgb) \>= 8g/dL * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Serum aspartate aminotransferase (serum glutamic oxalacetic transaminase \[SGOT\]/aspartate aminotransferase \[AST\]) or serum alanine aminotransferase (serum glutamate pyruvate transaminase \[SGPT\]/alanine aminotransferase \[ALT\]) =\< 3 x ULN * Serum creatinine =\< 2 x ULN * Prothrombin time (PT)/international normalized ratio (INR) =\< 1.5 * Have been informed of other treatment options * Patient or legal representative 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 * Have an Eastern Cooperative Oncology Group (ECOG) performance status of =\< 2 * The ability to swallow and retain oral medication * Patients of child-bearing potential must agree to use acceptable contraceptive methods (e.g., double barrier) during treatment * Patients may have received previous NY-ESO-1 vaccine therapy; patients who received maintenance paclitaxel or bevacizumab are eligible for enrollment provided they have discontinued therapy (at least 4 weeks for prior taxane) prior to randomization and recovered from toxicities to less than grade 2 Exclusion Criteria: * Metastatic disease to the central nervous system for which other therapeutic options, including radiotherapy, may be available * Other serious illnesses (e.g., serious infections requiring antibiotics, bleeding disorders) * History of autoimmune disease (e.g. thyroiditis, lupus) except vitiligo * Concomitant systemic treatment with corticosteroids, anti-histamine or non-steroidal anti-inflammatory drugs, and other platelet inhibitory agents * Chemotherapy, radiation therapy, or immunotherapy within 4 weeks prior to first dosing of study drug (6 weeks for nitrosoureas); concomitant hormonal therapies for breast cancers are allowed * Clinically significant heart disease (New York Heart Association \[NYHA\] class III or class IV) within 6 months * Participation in any other clinical trial involving another investigational agent within 4 weeks prior to first dosing of study drug * Known hepatitis B, hepatitis C, or human immunodeficiency virus (HIV) * Mental impairment that may compromise the ability to give informed consent and comply with the requirements of the study * Lack of availability of a patient for immunological and clinical follow-up assessment * Evidence of current drug or alcohol abuse or psychiatric impairment, which in the investigator's opinion will prevent completion of the protocol therapy or follow-up * Pregnant or nursing female patients * Unwilling or unable to follow protocol requirements * Any condition which in the investigator's opinion deems the patient an unsuitable candidate to receive study drug (i.e., any significant medical illness or abnormal laboratory finding that would, in the investigator's judgement, increase the patient's risk by participating in this study)