DNA Plasmid-encoding Interleukin-12/HPV DNA Plasmids Therapeutic Vaccine INO-3112 and Durvalumab in Treating Patients With Recurrent or Metastatic Human Papillomavirus Associated Cancers

Inclusion Criteria: * Written informed consent in accordance with institutional guidelines. * Are able and willing to comply with all study procedures. * For patients who are not human immunodeficiency virus (HIV) positive, cervical, anal, penile, vulvar, or vaginal cancer positive for HPV-16 and/or HPV-18 by the institutionally approved assay. For patients who are HIV positive, histologically or cytologically confirmed diagnosis of cancer at any site that is positive for HPV-16 and/or HPV-18 by the institutionally approved assay. Tumors may be positive for more than 1 HPV subtype as long as HPV-16 and/or HPV-18 is present. Note: For the first 3 patients, only cervical, vulvar, or vaginal cancers will be enrolled. * Patients with cancer that is refractory to standard therapy, that have either relapsed after standard therapy or has no standard therapy that increases survival by at least three months, and/or that are not curable by salvage approaches including resection and/or re-irradiation * Has measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) with a minimum size of 10 mm by computed tomography (CT) scan, except lymph nodes which must have minimum short axis size of 15 mm (CT scan slice thickness no greater than 5 mm in both cases). Indicator lesions must not have been previously treated with surgery, radiation therapy, or radiofrequency ablation unless there is documented Response …