Vaccine Therapy With or Without Sirolimus in Treating Patients With NY-ESO-1 Expressing Solid Tumors

Inclusion Criteria:

* Patients with any solid tumors at high risk of recurrence or with minimal residual disease; there may or may not be measurable or symptomatic disease (i.e., patients with bladder, brain, breast, esophageal, gastrointestinal, hepatocellular, kidney, lungs, melanoma, ovarian, prostate, sarcomas, and uterine)
* Cancer types:

  * Prostate cancer: patients with metastatic, castrate refractory prostate cancer; the use of luteinizing hormone-releasing hormone (LHRH) agonist is allowed
  * Kidney cancer: patients with metastatic kidney cancer; prior therapies with cytokines, vascular endothelial growth factor (VEGF) and mechanistic target of rapamycin (serine/threonine kinase) (mTOR) inhibitors are allowed
  * Bladder cancer: patients with metastatic urothelial carcinoma; prior cisplatin-based therapies are allowed
  * Ovarian cancer: 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 (CA)-125; or may be in complete clinical remission after treatment for primary or recurrent disease
  * Brain tumors: histologic proof of one of the following: glioblastoma multiforme, anaplastic astrocytoma, anaplastic oligodendroglioma or anaplastic mixed glioma or anaplastic oligoastrocytoma; patients who have had recent cranial surgery are eligible for inclusion, but the vaccine may not be administered prior to postoperative day 14
  * Uterine cancer: patients with advanced (stages II-IV) or recurrent disease who have completed standard therapy, currently no evidence of disease (NED) or with minimal residual disease; patients with stage I uterine serous carcinomas or sarcomas are also eligible after completion of standard therapy
  * Breast cancer: patients can enter study after completion of all chemotherapy (including trastuzumab), radiation, and breast/axillary surgery; patients may participate while on endocrine therapy; stages I-III patients with the following characteristics:

    * Estrogen-receptor (ER) negative with positive lymph nodes; ER negative with negative nodes if tumor \> 2 cm; ER positive with positive lymph nodes; and ER positive with negative lymph nodes and tumor \> 5 cm
  * Sarcomas: patients with sarcomas of any site, who have completed standard therapy, and are in remission, or have minimal disease burden
  * Lungs: resected patients with hilar or ipsilateral mediastinal nodal disease (i.e., a subset of patients with stage II and IIIA disease); and patients with residual disease on imaging after definitive radiation or chemoradiation therapy
  * Esophageal: resected patients with any nodal (i.e., thoracic or abdominal) disease; and patients with residual disease on imaging after definitive chemoradiation therapy
  * Melanoma: stage IIB, stage IIC, and stage III who have completed planned definitive therapy for their disease including radiotherapy and/or interferon; patients declining interferon or with contra-indications to interferon will also be eligible provided they meet requisite criteria for this study (i.e., non-measurable disease); stage IV melanoma of M1a sub-type only, who are not candidates for additional therapy of curative potential (i.e., small volume disease; may be measurable or evaluable); and stage IV melanoma, NED, status post (s/p) complete resection of known sites of disease (i.e., non-measurable disease)
  * Hepatocellular carcinoma (HCC): patients who have been treated with surgical resection for HCC; and following chemoembolization as adjuvant therapy for HCC
  * Gastrointestinal: patients who have completed standard therapies for gastric and colorectal cancers, and deemed to be at high-risk of relapse
* Any human leukocyte antigen (HLA) type; historic HLA typing is permitted
* Tumor expression of NY-ESO-1 or LAGE-1 by immunohistochemistry (IHC) and/or reverse transcription polymerase chain reaction (RTPCR)
* Life expectancy \> 6 months
* Absolute neutrophil count (ANC) \>= 1,000/uL
* Platelets (PLT) \>= 75,000/uL
* Hemoglobin (Hgb) \>= 8 g/dL
* Total bilirubin =\< 1.5 x upper limit of normal (ULN)
* Serum aspartate aminotransferase (serum glutamic oxaloacetic 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 x ULN; patients receiving anticoagulation therapy, PT/INR =\< 3
* Pulmonary function tests: forced expiratory volume in one second (FEV1) \> 50% and diffusion capacity of the lungs for carbon monoxide (DLCO) \> 50%
* Pulse oximetry: oxygen (O2) saturation \>= 90% on room air
* Electrocardiogram, showing no clinical significant or acute abnormality
* 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
* Patients of child-bearing potential must agree to use acceptable contraceptive methods (e.g., double barrier) during treatment

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 non-steroidal anti-inflammatory drugs, aspirin \> 325 mg; specific cyclooxygenase (COX)-2 inhibitors are permitted
* Chemotherapy, radiation therapy, or immunotherapy within 4 weeks prior to first dosing of study agent (6 weeks for nitrosoureas); concomitant hormonal therapies for breast and prostate cancers are allowed
* Clinically significant heart disease (New York Heart Association \[NYHA\] class III or IV) within 6 months
* 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)
* Received an investigational agent within 30 days prior to enrollment
* Known hepatitis B, hepatitis C, or human immunodeficiency virus (HIV)