A Study of Gebasaxturev (V937) in Combination With Pembrolizumab (MK-3475) in Participants With Advanced/Metastatic Solid Tumors (V937-013)

Inclusion Criteria: * Locally-advanced disease that is not amenable to surgery or radiation, or Stage IV advanced/metastatic solid tumor malignancies * Histologically- or cytologically-confirmed diagnosis of an advanced/metastatic solid tumor. * Measurable disease by RECIST 1.1 criteria as assessed by investigator. Target lesions in a previously irradiated area will be considered measurable if progression has been demonstrated in such lesions * Submitted a baseline tumor sample for analysis. Participants enrolling in Part 2 Cohorts D-F may enroll without submitting a tumor sample if all other enrollment criteria are met. * Performance status of 0 or 1 on the Eastern Cooperative Oncology Group (ECOG) Performance Scale obtained within 72 hours prior to the first dose of study intervention * If participant has known human immunodeficiency virus (HIV)-positive disease, participant must have well-controlled HIV on antiretroviral therapy (ART), per study criteria. * Adequate organ function * Male participants are eligible to participate if they agree to the following during the intervention period and for at least 120 days: Be abstinent from heterosexual intercourse as their preferred and usual lifestyle and agree to remain abstinent, OR must agree to use contraception unless confirmed to be azoospermic. * Female participants are eligible to participate if not pregnant or breastfeeding, and at least one of the following conditions applies: * Is not a woman of childbearing potential (WOCBP) * Is a WOCBP and using a contraceptive method that is highly effective, or be abstinent from heterosexual intercourse as their preferred and usual lifestyle (abstinent on a long term and persistent basis), during the intervention period and for at least 120 days after the last dose of study intervention. * Contraceptive use by women should be consistent with local regulations regarding the methods of contraception for those participating in clinical studies. * Part 1, All Cohorts: participants must have at least one injectable lesion amenable to injection and/or biopsy. * Part 1, Cohort A: * Locally recurrent, inoperable OR metastatic breast cancer treated with at least 1 prior line of therapy in the metastatic setting with skin involvement and/or subcutaneous lesions or accessible lymph nodes amenable to local injection. An exception would be allowed for participants who are not eligible to receive chemotherapy. * Diagnosis of triple-negative breast cancer (estrogen receptor, progesterone receptor, and HER2-receptor negative status) * Part 1, Cohort B: * Histologically confirmed advanced or metastatic head and neck squamous cell carcinoma (HNSCC) of the oral cavity, oropharynx, hypopharynx, and/or larynx considered incurable and/or treated with no more than 1 previous line of therapy * Tumors must be PD-L1+ * Documentation of HPV status for oropharyngeal cancers. Other HNSCC subtypes may submit HPV testing, but is not required. * Part 1, Cohort C: * Histologically confirmed cutaneous squamous cell carcinoma (cSCC) as the primary site of malignancy * Recurrent/metastatic disease only: Has metastatic disease defined as disseminated disease distant from the initial/primary site of diagnosis and/or with a history of locally-recurrent disease previously treated with surgery and/or radiotherapy, which is now incurable * Locally-advanced disease only: Must be ineligible for surgical resection per study criteria, and must have received prior radiation therapy to the index site or deemed ineligible for radiation therapy * Part 2, Solid Tumors+Liver Metastases Dose Level 1-3 arms: * Histologically-confirmed advanced/metastatic solid tumor that has progressed on all treatment known to confer clinical benefit * Metastatic liver lesion(s) not exceeding one-third of the total liver volume AND a minimum of one injectable liver lesion * Part 2, Cohort D: * Advanced hepatocellular carcinoma (HCC) following progression on, or intolerance to, sorafenib or lenvatinib with no curative options * Diagnosis of HCC confirmed by radiology, histology, or cytology * Child-Pugh Class A score * If a participant has a history of hepatitis C virus (HCV) infection, then the participant must have been successfully treated for this condition * Controlled (treated) hepatitis B participants will be allowed if they meet protocol-specified criteria * Participants who are anti-hepatitis B core (HBc) positive, negative for hepatitis B surface antigen (HBsAg), negative or positive for anti-hepatitis B surface (HBs), and who have an HBV viral load under 100 IU/mL, do not require HBV anti-viral prophylaxis * Part 2, Cohort E: * Histologically- or cytologically-confirmed diagnosis of locally advanced, unresectable or metastatic gastric or gastroesophageal junction (GEJ) adenocarcinoma * Received at least one prior line of therapy that includes a platinum/fluoropyrimidine doublet or triplet regimen * Had proven clinical progression 6 months following (or during) last dose of adjuvant or neo-adjuvant therapy * Human epidermal growth factor receptor 2 (HER2) negative status; or, those with HER2 positive status AND documented disease progression on a prior regimen containing trastuzumab Exclusion Criteria: * Chemotherapy, definitive radiation, or biological cancer therapy within 4 weeks (2 weeks for palliative radiation) prior to first dose of study intervention, or has not recovered to Common Terminology Criteria for Adverse Events (CTCAE) Grade 1 or better * If major or minor surgery was performed at/near the area being considered for injection, participant must be recovered from toxicity and/or complications of intervention * If participant has had injection or radiation therapy, participant must be recovered from toxicity and/or complications of intervention * History of second malignancy, unless potentially curative treatment has been completed with no further evidence of disease for ≥5 years. * Known active central nervous system (CNS) metastases and/or carcinomatous meningitis. Participants with treated brain metastases may participate if lesions are radiologically stable. * Active infection requiring therapy, except HIV criteria as stated above, and HBV and HCV criteria for HCC cohort as stated above * History of interstitial lung disease * History of noninfectious pneumonitis requiring active steroid therapy or ongoing pneumonitis * Active autoimmune disease that required systemic treatment in the past 2 years except vitiligo or resolved childhood asthma/atopy * Known Hepatitis B or C infections or known to be positive for HBsAg/HBV deoxyribonucleic acid (DNA) or Hepatitis C Antibody or ribonucleic acid (RNA) * History of Kaposi's sarcoma and/or Multicentric Castleman's Disease * Known hypersensitivity to gebasaxturev and/or pembrolizumab or any of their excipients * Received prior therapy with anti-programmed cell death protein-1 (anti-PD-1), anti-programmed cell death-ligand 1 (anti-PD-L1) agents, Talimogene Laherparepvec (T-VEC), or any other oncolytic virus therapies * Received a live or live-attenuated vaccine within 30 days prior to first dose of study intervention. Administration of killed vaccines is allowed. * Pregnant or breastfeeding or expecting to conceive or father children within the projected duration of the study, starting with the screening visit through 120 days after the last dose of study intervention * Part 2, Cohort D: * Has had esophageal or gastric variceal bleeding within the last 6 months * Has had clinically diagnosed hepatic encephalopathy in the 6 months prior to initiation of study intervention * Part 2, Cohort E: * Squamous cell or undifferentiated gastric cancer