This is a Trial of MG1-E6E7 With Ad-E6E7 and Atezolizumab in Patients With HPV Associated Cancers

Key Inclusion Criteria: * Histologically or cytologically confirmed recurrent or metastatic HPV associated tumor (cervical, oropharyngeal, vulvar, vaginal, anal, or penile) with documented disease progression. * Arm 1, Phase 1 dose escalation: Cervical, HPV+ oropharyngeal, vulvar, vaginal, anal, or penile * Arm 1, Cohort A: Cervical cancer * Arm 1, Cohort B: HPV+ Oropharyngeal cancer * Arm 2 Phase 1 dose escalation and Cohort C: Cervical, oropharyngeal, vulvar, vaginal, anal, or penile * Failed, refused or intolerant to systemic therapy * Measurable disease based on RECIST 1.1 * At least one tumor mass amenable to core needle biopsy * Arm 2 only: At least one tumor judged as being safely injectable * ECOG performance status 0 or 1 * Demonstrate adequate organ function * Additional Inclusion criteria exist Key Exclusion Criteria: * Prior systemic therapy within 4 weeks. * Patients receiving prior XRT must have recovered from any acute toxicity. * Currently receiving/received experimental therapy within 4 weeks. * Prior treatment with any HPV vaccine therapy for cancer. * Requires use of anti-platelet or anti-coagulant therapy that cannot be safely suspended for per protocol biopsies or intra-tumoral injections. * Known active CNS metastases and/or carcinomatous meningitis. * Clinically significant tumor invasion/ rapidly accumulating ascites, pericardial or pleural effusions. * Active infection requiring systemic therapy. * Active autoimmune disease that has required systemic therapy in the past 2 years. * Conditions likely to have resulted in splenic dysfunction. * Known HIV/AIDS, active HBV or HCV infection. * Received prior treatment with vesicular stomatitis (VSV) viral vector. * Received immunosuppressive medication within 4 weeks. (\>10mg/day prednisone) * ≥ Grade 2 dyspnea and/or require supplemental oxygen * Known intolerance to anti-PD-1 or anti-PD-L1 antibody therapy * Additional Exclusion criteria exist Exclusion Criteria Household Contacts: * Patients with household contacts meeting any of the following criteria are ineligible for study entry unless alternate living arrangements can be made, while under contact precautions. * Women who are pregnant or nursing an infant * Children \< 1 year old * Individuals who are severely immunocompromised * Contact precautions are from initial treatment with MG1-E6E7 to 7 days after the last dose of MG1-E6E7