Testing the Addition of the Anti-cancer Viral Therapy Telomelysin™ to Chemoradiation for Patients With Advanced Esophageal Cancer and Are Not Candidates for Surgery

Inclusion Criteria: * Pathologically (histologically or cytologically) proven diagnosis of adenocarcinoma or squamous cell carcinoma (SCC) of the esophagus or gastroesophageal junction (GEJ) within 90 days prior to registration * Gastroesophageal junction tumors must be Siewert type I/II * Required diagnostic workup for study entry: * History/physical examination prior to registration * Computed tomography (CT) of the chest/abdomen with intravenous contrast within 28 days prior to registration; If CT contrast is contraindicated magnetic resonance imaging (MRI) of the chest/abdomen without contrast is permitted * Bronchoscopy for squamous cell carcinoma (SCC) tumors that are adjacent to the airway to exclude a tracheoesophageal fistula within 42 days prior to registration * Endoscopic ultrasound (if technically feasible) within 90 days prior to registration * Whole body positron emission tomography (PET)/CT scan within 42 days prior to registration: Note: scan will be used for radiation treatment planning, in addition to ruling out metastatic disease * Eastern Cooperative Oncology Group (ECOG) performance status of 0-2 within 14 days prior to registration * Adequate hematologic function within 14 days prior to registration defined as follows Absolute neutrophil count ≥ 1,500/mcL (within 14 days prior to registration) Hemoglobin ≥ 9 gm/dL (within 14 days prior to registration) Platelets ≥ 100,000/mcL (within 14 days prior to registration) * Adequate renal function within 14 days prior to registration defined as follows Creatinine clearance of ≥ 50 ml/min (as calculated by Cockcroft-Gault equation) (within 14 days prior to registration) * Total bilirubin ≤ 1.5 x upper limit of normal (ULN) (within 14 days prior to registration) * AST/ALT ≤ 2.5 x ULN * Patients for whom non-operative management is a viable option in the opinion of a thoracic surgeon and/or multidisciplinary team and are candidates for chemoradiation; this does not preclude patients from receiving surgery after chemoradiation if felt to me medically indicated; * Patients must, in the opinion of a treating gastroenterologist, have a tumor that is amenable to intratumoral injection with at least 1 mL (1 x 10\^12 vp/mL) of OBP-301 and be a candidate for 3 endoscopy procedures * Female patients of child bearing potential must have a negative serum/urine pregnancy test within 14 days prior to study entry. A female not of childbearing potential is one who has undergone a hysterectomy, bilateral oophorectomy, tubal ligation, or who has had no menses for 12 consecutive months * Patients of reproductive potential must agree to use effective contraception for the duration of study treatment as well as 6 months (for women) or 12 months (for men) after the last administered injection of OBP-301. Effective contraception includes oral contraceptives, implantable hormonal contraception, double-barrier method or intrauterine device * The patient must provide study-specific informed consent prior to study entry * Patients with a prior or concurrent malignancy whose natural history or treatment does not have the potential to interfere with the safety or efficacy assessment of the investigational regimen are eligible for this trial * Known acute or chronic hepatitis B or C infection (testing not required prior to study entry in patients with no known history of hepatitis B or C) * For patients with evidence of chronic hepatitis B virus (HBV) infection, the HBV viral load must be undetectable on suppressive therapy, if indicated * For patients with a history of hepatitis C virus (HCV) infection, they must (i) have been treated and cured, (ii) for patients with HCV infection who are currently on treatment, they are eligible if they have an undetectable HCV viral load * Human immunodeficiency virus (HIV)-infected patients on effective anti-retroviral therapy with undetectable viral load within 6 months prior to study entry are eligible for this trial Exclusion Criteria: * Definitive clinical or radiologic evidence of metastatic disease including: * Positive malignant cytology of the pleura, pericardium or peritoneum * Radiographic evidence of involvement of any adjacent mediastinal structure, e.g. aorta, trachea, which would increase the risk of repeated endoscopic interventions * Tracheoesophageal fistula * Radiographic evidence of distant organ involvement * Non-regional lymph nodes that cannot be contained within a radiation field * More than 1 esophageal lesion * Prior systemic chemotherapy for the study cancer * Prior radiotherapy to the region of the study cancer that would result in overlap of radiation therapy fields * Biopsy-proven tumor invasion of the tracheobronchial tree or presence of tracheoesophageal fistula or recurrent laryngeal or phrenic nerve paralysis * For patients with known history or current symptoms of cardiac disease, or history of treatment with cardiotoxic agents, a New York Heart Association functional classification 2C or worse * Uncontrolled diabetes * Infection requiring IV antibiotics at the time of registration * Patients requiring immunosuppressive medications including chronic suppressive steroid therapy (greater than the equivalent of 20 mg/day of prednisone), methotrexate, azathioprine and TNF-alpha blockers within 7 days prior to study entry * Received live vaccine within 30 days prior to registration * Received a blood transfusion, hematopoietic agent; granulocyte-colony stimulating factor (G-CSF), and/or oxygen supplementation within 7 days before the screening lab * Breast feeding females