Modified Virus VSV-IFNbetaTYRP1 in Treating Patients With Stage III-IV Melanoma

Inclusion Criteria: * Age \>= 18 years * Histologically or cytologically confirmed diagnosis of unresectable stage III or metastatic (stage IV) melanoma, including metastatic ocular melanoma * Cutaneous melanoma patients only: * At least one prior Food and Drug Administration (FDA) approved systemic therapy in the metastatic setting; and disease progression after immune checkpoint inhibitors * If tumor is BRAF-mutated, previous BRAF- and/or MEK-targeted therapies are required * NOTE: for ocular melanoma patients no current standard of care exists, so patients are permitted to be treated in 1st line setting * Measurable disease by any imaging modality as defined by Response Evaluation Criteria in Solid Tumors (RECIST) (version 1.1) * NOTE: disease that is measurable by physical examination only is not eligible * Injectable disease (i.e., suitable for direct injection or through the use of ultrasound guidance) defined as: * At least 1 injectable and safely accessible cutaneous, subcutaneous, or nodal melanoma lesion \>= 5 mm in longest diameter for metastatic cutaneous or mucosal melanoma * At least one safely accessible liver metastasis for patients with metastatic ocular melanoma * Patients with metastatic ocular melanoma must meet all of the additional inclusion criteria: * No more than 25% overall tumor involvement of the liver by magnetic resonance imaging (MRI) imaging * Child Pugh Score A * Absence of ascites * No portal vein thrombosis * Have re…