Sirolimus and Vaccine Therapy in Treating Patients With Stage II-IV Ovarian Epithelial, Fallopian Tube, or Primary Peritoneal Cavity Cancer

Inclusion Criteria: * Eligible patients will be women with stages II-IV epithelial ovarian, fallopian tube, or primary peritoneal carcinoma who have completed standard therapy for primary or recurrent disease (i.e., patients who would normally be observed); eligible patients may have asymptomatic residual measurable disease on physical examination and/or computed tomography (CT) scan, and/or may have an elevated cancer antigen 125 (CA-125); or may be in complete clinical remission after treatment for primary or recurrent disease; 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 real-time polymerase chain reaction (RT-PCR) * 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 \>= 75,000/uL * Hemoglobin (Hgb) \>= 8 g/dL * Total bilirubin =\< 1.5 x upper limit of normal (ULN) * Serum glutamic oxaloacetic transaminase (SGOT)/aspartate aminotransferase (AST) or serum glutamic pyruvic transaminase (SGPT)/alanine aminotransferase (ALT) =\< 3 x ULN * Serum creatinine =\< 2 x ULN * Prothrombin time (PT)/international normalized ratio (INR) =\< 1.5 * Electrocardiogram, showing no evidence of congestive heart failure, myocardial infarction, and cardiomyopathy * 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 * Demonstrate 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 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 severe autoimmune disorders requiring use of steroids or other immunosuppressives * Concomitant systemic treatment with corticosteroids, anti-histamine or nonsteroidal anti-inflammatory drugs and other platelet inhibitory agents, strong inhibitors/inducers of cytochrome P450, family 3, subfamily A, polypeptide 4 (CYP450-3A4) * 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 * Known allergy or history of life threatening reaction to GM-CSF * Clinically significant heart disease (N-YHA Class III or IV) * 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 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 * Known pulmonary hypertension * Known hypersensitivity to sirolimus * 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 judgment, increase the subject's risk by participating in this study)