Optimizing Antitumor Immunity Using Plasmid Electroporation, Pembrolizumab, and Epacadostat

Inclusion Criteria: * Age \>= 18 years old. * Eastern Cooperative Oncology Group (ECOG) performance status 0-2. * Life expectancy of at least 4 months. * Patients must have histological or cytological diagnosis of cancer originating in the head and neck that is not amenable to surgical resection or locoregional radiation therapy with curative intent. * At least one accessible lesion (AL) for intratumoral injection. An AL is defined as meeting the following criteria; (1) at least 0.3 cm x 0.3 cm in longest perpendicular diameters (2) in a suitable location for application of electroporation. Tumors invading the carotid artery or at other sites that the investigator believes to be at high risk of life-threatening hemorrhage should not be injected and these lesions may not be used to meet the inclusion criterion for injectable lesions. * Measurable disease as defined by Response Evaluation Criteria in Solid Tumors (RECIST) v1.1; at least one lesion where the longest perpendicular diameter is at least 1.0 cm by clinical measurement; or at least 1.0 cm by radiographic imaging for non-nodal lesions; at least 1.5 cm in short axis by radiographic imaging for malignant lymph nodes; If the biopsied lesions were previously irradiated, they must demonstrate either radiographic or pathological evidence of recurrent or residual disease. It is not necessary that this lesion is also an AL. * If patient has known brain metastases, they must have stable neurologic status following local therapy (surgery or radiation) for at least 4 weeks without the use of steroids or on stable or decreasing dose of \<=10 mg daily prednisone (or equivalent), and must be without neurologic dysfunction that would confound the evaluation of neurologic and other adverse events (AEs) (patients with a history of carcinomatous meningitis are not eligible). * Patients may have had prior chemotherapy or immunotherapy or radiation therapy. Any drug related adverse events identified during prior therapy must be well controlled (typically resolution to =\< grade 1, OR resolved upon investigator review prior to initiation of this therapy. * No systemic antineoplastic therapy may be received by the patient between the time of the biopsy and the first administration of study treatment. * Patient must agree to any protocol mandated biopsies of tumor (deemed accessible and safe for biopsy by the investigator's assessment) and they must allow acquired tissue to be used for biomarker analysis. * For women of childbearing potential, negative serum or urine pregnancy test within 14 days of first dose of study drug(s) and use of birth control from 30 days prior to the first study drug administration and 120 days following last administration of study drug, or for participants in Arm C, 180 days after last dose of CORVax, whichever is longer. * Male patients must be surgically sterile or must agree to use contraception during the study and at least 120 days following the last administration of study drug, or for participants in Arm C, 180 days after last dose of CORVax, whichever is longer. Exclusion Criteria: * Active autoimmune disease that has required systemic treatment in past 2 years. Replacement therapy (e.g., thyroxine, insulin, or physiologic corticosteroid replacement therapy for adrenal or pituitary insufficiency) is not considered a form of systemic treatment. * Congestive heart failure (New York Heart Association class III to IV) * History or presence of an abnormal electrocardiogram (ECG) that, in the investigator's opinion, is clinically meaningful. Screening corrected QT (QTc) interval \> 480 milliseconds is excluded. In the event that a single QTc is \> 480 milliseconds, the subject may enroll if the average QTc for the 3 ECGs is \< 480 milliseconds. For subjects with an intraventricular conduction delay (QRS interval \> 120 milliseconds), the corrected JT (JTc) interval may be used in place of the QTc with sponsor approval. The JTc must be \< 340 milliseconds if JTc is used in place of the QTc. Subjects with left bundle branch block are excluded. * Uncontrolled or clinically significant conduction abnormalities (e.g., ventricular tachycardia on anti-arrhythmics are excluded), 1st degree atrioventricular (AV) block or asymptomatic left anterior fascicular block (LAFB)/right bundle branch block (RBBB) are eligible. * Uncontrolled, symptomatic ischemia within 6 months of first dose of study treatment or known myocardial infarction in the previous six months. * Patients with electronic pacemakers or defibrillators. * Has history of (non-infectious) pneumonitis/interstitial lung disease that required steroids or has current pneumonitis/interstitial lung disease. * Any other current or previous malignancy within the past 2 years that, in the opinion of the principal investigator will interfere with study-specific endpoints. * Evidence of significant active infection (e.g., pneumonia, cellulitis, wound abscess, etc.) requiring systemic therapy at time of study enrollment. * Hepatitis B: Most nasopharyngeal cancer (NPC) patients have been infected with hepatitis B (Cancer Epidemol Biomarkers Prev. 2015. 24:1766-73, N = 711) and, therefore, the inclusion of healthy patients with a history of hepatitis B is a central part of this study. In addition, programmed cell death protein 1 (PD-1) antibodies have been proven to be safe in patients with active hepatitis and hepatocellular carcinoma (e.g. KEYNOTE 224). However, patients with hepatitis B virus (HBV) surface antigen positive (HBSAg) must have aspartate aminotransferase (AST) and total bilirubin \< 1.5 x upper limit of normal (ULN) AND * Negative HBV ribonucleic acid (RNA) polymerase chain reaction (PCR) OR * On antivirals for HBV AND at least 8 weeks of prior anti-PD-1 antibody therapy AND no history of AST or total bilirubin levels \> 1.5 x ULN due to PD-1 antibody therapy * Hepatitis C (hepatitis C virus (HCV) RNA (qualitative) is detected). * Presence of a gastrointestinal condition that may affect drug absorption. Administration of epacadostat through a feeding tube is permitted. * Patients receiving systemic steroid therapy for a chronic inflammatory condition. Topical steroids, nasal and inhaled steroids are permitted. Prednisone or equivalent =\< 10 mg/day is permitted as hormone replacement; higher dosage prednisone should be stopped at least 14 days prior to course 1 day 1 (C1D1). * Receipt of a live vaccine or live attenuated vaccine within 30 days before the first dose of study treatment. Administration of killed vaccines is allowed. * Subjects receiving monoamine oxidase inhibitors (MAOIs) or drug which has significant MAOI activity (meperidine, linezolid, methylene blue) within the 21 days before screening. * Any history of serotonin syndrome (SS) after receiving serotonergic drugs. * Use of any uridine 5'-diphospho-glucuronosyltransferase 1-9 (UGT1A9) inhibitor from screening through follow-up period, including the following: diclofenac, imipramine, ketoconazole, mefenamic acid, and probenecid. * Known allergy or reaction to any component of study drug formulation. * Absolute neutrophil count (ANC) \< 1.0 x 10\^9/L. * Platelets \< 75 x 10\^9/L. * Hemoglobin \< 9 g/dL or \< 5.6 mmol/L (transfusion is acceptable to meet this criterion). * Serum creatinine \>= 1.5 x institutional upper limit of normal (ULN) OR measured or calculated creatinine clearance \[glomerular filtration rate can also be used in place of creatinine or creatinine clearance (CrCl)\] \< 50 mL/min for subjects with creatinine levels \> 1.5 x institutional ULN. * Aspartate aminotransferase (AST) or alanine aminotransferase (ALT) \> 2.5 x institutional ULN. * Alkaline phosphatase \> 2.5 x ULN. Note: Subjects with 1) bone metastases and gamma-glutamyl transpeptidase (GGT) \< 2.5 x ULN may enroll if the alkaline phosphatase is \< 5 x ULN. * Total bilirubin above 1.5 x the institutional ULN AND conjugated bilirubin \>= 2.0 x ULN. * International normalized ratio (INR) or prothrombin time (PT) \> 1.5 x ULN. * Activated partial thromboplastin time (aPTT) \> 1.5 x ULN.