Viral Therapy in Treating Young Patients With Relapsed or Refractory Solid Tumors

Inclusion Criteria: * Patients with relapsed or refractory solid tumors, with the exception of central nervous system (CNS) tumors and lymphomas, are eligible; patients must have had histologic verification of malignancy at original diagnosis or relapse * Patients must have either measurable or evaluable disease * Patient's current disease state must be one for which there is no known curative therapy or therapy proven to prolong survival with an acceptable quality of life * Karnofsky \>= 50 for patients \> 16 years of age and Lansky \>= 50 for patients =\< 16 years of age; patients who are unable to walk because of paralysis, but who are up in a wheelchair, will be considered ambulatory for the purpose of assessing the performance score * Patients must have fully recovered from the acute toxic effects of all prior anti-cancer chemotherapy and immunizations * Must not have received myelosuppressive chemotherapy within 3 weeks of enrollment onto this study (6 weeks if prior nitrosourea) * At least 14 days after the last dose of a long-acting growth factor (e.g. Neulasta) or 7 days for short-acting growth factor; for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur; the duration of this interval must be discussed with the study chair * At least 7 days after the last dose of a biologic agent; for agents that have known adverse events occurring beyond 7 days after administration, this period must be extended beyond the time during which adverse events are known to occur; the duration of this interval must be discussed with the study chair * At least 6 weeks since the completion of any type of immunotherapy, e.g. tumor vaccines * At least 3 half-lives of the antibody after the last dose of a monoclonal antibody * \>= 2 weeks for local palliative radiation therapy (XRT) (small port); \>= 24 weeks must have elapsed if prior total-body irradiation (TBI), craniospinal XRT or if \>= 50% radiation of pelvis; \>= 6 weeks must have elapsed if other substantial bone marrow (BM) radiation * No evidence of active graft vs host disease and \>= 12 weeks must have elapsed since stem cell transplant or infusion * Patients must not have received any previous viral-based anti-neoplastic therapies * Viral immunizations, including influenza, may not have been administered within 7 days prior to enrollment; Note: patients may not receive any viral immunizations after enrolling on study until 28 days post their last planned REOLYSIN infusion * Peripheral absolute neutrophil count (ANC) \>= 1000/mm\^3 * Platelet count \>= 100,000/mm\^3 (transfusion independent (transfusion independent, defined as not receiving platelet transfusions within a 7 day period prior to enrollment) * Patients with known bone marrow metastatic disease will be eligible for study but not evaluable for hematologic toxicity (maximum of one per cohort); such patients must meet the blood counts above (may receive transfusions provided they are not be known to be refractory to red cell or platelet transfusion); if dose-limiting hematologic toxicity is observed, all subsequent patients enrolled must be evaluable for hematologic toxicity * Creatinine clearance or radioisotope glomerular filtration rate (GFR) \>= 70 mL/min OR serum creatinine based on age and/or gender as follows: * 0.8 mg/dL (3 to \< 6 years of age) * 1.0 mg/dL (6 to \< 10 years of age) * 1.2 mg/dL (10 to \< 13 years of age) * 1.5 mg/dL (male) or 1.4 mg/dL (female) (13 to \< 16 years of age) * 1.7 mg/dL (male) or 1.4 mg/dL (female) (\>= 16 years of age) * Bilirubin (sum of conjugated plus unconjugated) =\< 1.5 x upper limit of normal (ULN) for age * Serum glutamate pyruvate transaminase (SGPT) (alanine aminotransferase \[ALT\]) =\< 110 U/L; for the purpose of this study, the ULN for SGPT is 45 U/L * Serum albumin \>= 2 g/dL * Shortening fraction \>= 27% by echocardiogram OR ejection fraction \>= 50% by gated radionuclide study * Normal pulmonary function tests (PFTs) (including diffusion capacity of carbon monoxide \[DLCO\]) if there is clinical indication for determination (e.g. dyspnea at rest, known requirement for supplemental oxygen); for patients who do not have respiratory symptoms, full PFTs are NOT required * Patients with seizure disorder may be enrolled if on anticonvulsants and well controlled * Nervous system disorders National Cancer Institute (NCI) Common Terminology Criteria for Adverse Events version 4 (CTCAE v. 4) resulting from prior therapy must be =\< grade 2 * All patients and/or their parents or legally authorized representatives must sign a written informed consent; assent, when appropriate, will be obtained according to institutional guidelines Exclusion Criteria: * Pregnant or breast-feeding women will not be entered on this study due to risks of fetal and teratogenic adverse events as seen in animal/human studies; pregnancy tests must be obtained in girls who are post-menarchal; males or females of reproductive potential may not participate unless they have agreed to use an effective contraceptive method * Patients who have an uncontrolled infection are not eligible * Patients with chronic diarrhea, urinary incontinence during the day or at night, or patients who are not completely toilet trained will not be eligible * Patients will be excluded if they have household contacts who are pregnant, immunosuppressed or infants less than 3 months of age; household contacts are defined as anyone living with the patient during the isolation period of the treatment cycles * Patients who in the opinion of the investigator may not be able to comply with the safety monitoring requirements of the study are not eligible * Patients with known human immunodeficiency virus (HIV) or hepatitis B or C are excluded due to risk of viral infectivity of REOLYSIN; therefore, patients with a pre-existent infection are not eligible * Patients who are currently receiving other anti-cancer agents are not eligible * Patients who are currently receiving another investigational drug are not eligible * Patients who are receiving cyclosporine, tacrolimus or other agents to prevent either graft-versus-host disease post bone marrow transplant or organ rejection post transplant are not eligible for this trial * Patients must not have received corticosteroids, immune modulators or antiviral therapy for 7 days prior to enrollment and must not have an anticipated need for any of these therapies, intravenous immune globulin (IVIG) must not have been administered within 2 weeks prior to enrollment * Patients should avoid taking acetaminophen with REOLYSIN; whenever suitable, physicians should utilize alternative medications * Patients with known germline mutations affecting Ras activation (e.g. NF-1, Cardio-facial-cutaneous syndrome, Noonan syndrome, Costello syndrome) will be excluded from enrollment * Patients with known metastatic CNS disease involvement are excluded * Patients with primary CNS tumors are excluded