A Vaccine (PDS0101) Alone or in Combination With Pembrolizumab for the Treatment of Locally Advanced Human Papillomavirus-Associated Oropharynx Cancer

Inclusion Criteria: * Age \>= 18 years * Disease characteristics * Locally advanced HPV-OPSCC and high-risk HPV-specific testing with at least one of the following: * Radiology extranodal extension (ENE) OR * cN2 (AJCC 8th Edition) disease (contralateral/bilateral nodes) OR * cN3(AJCC 8th Edition) disease (lymph node \[LN\] \> 6 cm) OR * Radiographic evidence of 2 or more involved lymph nodes * Candidate for curative intent surgery or chemo-radiation * Measurable or unmeasurable disease as defined by RECIST 1.1 criteria * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * White blood cell (WBC) count \>= 3,000/mm\^3 (=\< 15 days prior to registration) * Platelet count \>= 75,000/mm\^3 (=\< 15 days prior to registration) * Hemoglobin \>= 9.0 g/dL (5.6 mmol/L) (=\< 15 days prior to registration) * NOTE: Transfusions are not allowed =\< 7 days prior to registration * Total bilirubin =\< 1.5 X upper limit of normal (ULN) (or total bilirubin =\< 3.0 X ULN with direct bilirubin =\<1.5 X ULN in patients with well-documented Gilbert's Syndrome) (=\< 15 days prior to registration) * Aspartate aminotransferase/serum glutamic-oxaloacetic transaminase (AST/SGOT) =\< 2.5 X ULN (=\< 15 days prior to registration) * Creatinine =\< 1.5 mg/dL (133 umol/L) OR calculated creatinine clearance \>= 30 mL/min/1.73m\^2 for patients with creatinine levels above ULN (=\< 15 days prior to registration) * Prothrombin time (PT)/international normalized rati…