Recombinant Measles Virus Vaccine Therapy and Oncolytic Virus Therapy in Treating Patients With Progressive, Recurrent, or Refractory Ovarian Epithelial Cancer or Primary Peritoneal Cancer

Inclusion criteria: * Age ≥ 18 years. * Must have persistent, recurrent or progressive ovarian cancer or primary peritoneal cancer after prior treatment with platinum and taxol compounds. Histologic confirmation of the original primary tumor is required. Prior bilateral oophorectomy is required. * Patients with the following histologic epithelial cell types are eligible: Serous adenocarcinoma, endometroid adenocarcinoma, mucinous adenocarcinoma, undifferentiated carcinoma, clear cell adenocarcinoma, mixed epithelial carcinoma, transitional cell carcinoma, malignant Brenner's Tumor, or adenocarcinoma NOS * The following laboratory values obtained ≤7 days prior to registration: * ANC ≥ 1500/μL * PLT ≥ 100,000/μL * Total bilirubin ≤ upper normal limit * AST ≤ 2 x ULN * Creatinine ≤ 1.5 x ULN * Hgb ≥ 9.0 g/dL * Ability to provide informed consent. * Willingness to return to Mayo Clinic Rochester for follow-up. * Life expectancy ≥ 12 weeks. * Must have anti-measles immunity as demonstrated by serum IgG anti-measles antibody levels of ≥ 20.0 EU/ml as determined by Enzyme Immunoassay (Diamedix, FL). * Must have normal serum CEA levels (\<5 mg/ml) both at the time of study entry and in any prior testing. (NOTE: Not applicable for the MV-NIS cohort.) * Willingness to provide all biologic specimens as required by the protocol. * Measurable disease by exam or CT scan, or, for patients with CA-125 elevation or with microscopic residual but without measurable disease on imag…