Viral Therapy in Treating Patients With Ovarian Epithelial Cancer, Primary Peritoneal Cancer, or Fallopian Tube Cancer That Did Not Respond to Platinum Chemotherapy

Inclusion Criteria: * Histologically confirmed ovarian epithelial, primary peritoneal, or fallopian tube cancer * Recurrent disease after platinum-based chemotherapy * Must have experienced disease persistence during primary platinum-based therapy or recurrence within 12 months after completion of platinum-based chemotherapy ("platinum-refractory" or "platinum-resistant" disease) * A patient receiving a second course of platinum-based chemotherapy for platinum-sensitive disease who then develops persistence or recurrence within 12 months is considered eligible for this trial * Must have measurable disease by RECIST criteria (phase II) (phase II closed as of 1/7/2011) * Must have received ≥ 1 prior platinum-based cytotoxic chemotherapy regimen (for primary disease) containing carboplatin, cisplatin, or other organoplatinum compound * Initial treatment may have included any of the following: * High-dose therapy * Consolidation therapy * Intraperitoneal (IP) therapy * Extended therapy administered after surgical or nonsurgical assessment * One additional non-cytotoxic regimen (e.g., monoclonal antibodies, cytokines, or small-molecule inhibitors) for recurrent or persistent disease allowed * Patients may have received hormonal therapy for management of disease (e.g., SERMs, aromatase inhibitors, progestins, and GnRH agonists) * No loculated ascites for which IP distribution of virus is not expected to be feasible * No known brain metastases * GOG performance status (PS) 0-2 (Karnofsky PS 60-100%) * Life expectancy \> 12 weeks * Leukocytes ≥ 3,000/mcL * Absolute neutrophil count ≥ 1,500/mcL * Hemoglobin ≥ 10 g/dL * Platelets ≥ 100,000/mcL * Total bilirubin normal * AST/ALT ≤ 2.5 times upper limit of normal * Creatinine normal * Ejection fraction \> 50% by echocardiogram or MUGA * Cardiac enzymes normal * Not pregnant or nursing * Fertile patients must use adequate contraception (hormonal or barrier method of birth control or abstinence) prior to study entry and for the duration of study participation * Must be able to avoid direct contact with pregnant or nursing women, infants, or immunocompromised individuals while on study and for ≥ 3 weeks following the last dose of study agent administration * Cardiac conduction abnormalities (e.g., bundle branch block, heart block) are allowed if their cardiac status has been stable for 6 months before study entry * At least 4 weeks since most recent cytotoxic chemotherapy (6 weeks for nitrosoureas or mitomycin C) * Recovered from adverse events due to agents administered more than 4 weeks earlier * No prior radiotherapy to the abdomen or pelvis * No other concurrent investigational agents * No investigational or commercial agents or therapies other than those described below may be administered with the intent to treat the patient's malignancy Exclusion Criteria: * Patients in whom insertion of an IP catheter is not feasible due to surgical contraindications or abdominal and pelvic adhesions * Known HIV infection or hepatitis B or C * Clinically significant cardiac disease (New York Heart Association class III or IV cardiac disease) including any of the following: * Pre-existing arrhythmia * Uncontrolled angina pectoris * Myocardial infarction 1 year prior to study entry * Compromised left ventricular ejection fraction ≥ grade 2 by MUGA or echocardiogram * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, or psychiatric illness/social situations that would limit compliance with study requirements * Chronic oral steroids at an equivalent dose of prednisone 5 mg daily * Inhaled steroids allowed * Patients on immunosuppressive therapy * Concurrent routine prophylactic use of growth factor (filgrastim \[G-CSF\] or sargramostim \[GM-CSF\])