Pralatrexate and Oxaliplatin in Treating Patients With Unresectable or Metastatic Esophageal, Stomach, or Gastroesophageal Junction Cancer

Inclusion Criteria: * Histologically confirmed carcinoma of the esophagus, stomach or gastro-esophageal junction that is metastatic, or locally advanced and inoperable for cure; histological sub-types permitted include adenocarcinoma, squamous-cell carcinoma, or undifferentiated carcinoma; small-cell carcinoma variant is not eligible * No previous systemic therapy for metastatic or recurrent disease; therapy (chemotherapy, radiotherapy, or both) administered in the neo-adjuvant, adjuvant, or definitive setting for previously localized disease is permitted, provided it was completed more than 6 months prior to enrollment; palliative radiotherapy is permitted provided it is completed \>= 3 weeks prior to study therapy initiation * Eastern Cooperative Oncology Group (ECOG) performance status 0-2 * Life expectancy \>= 12 weeks * Hemoglobin \>= 9 g/dl * Absolute neutrophil count \>= 1500/mm\^3 * Platelet count \>= 100,000/mm\^3 * Serum creatinine =\< institutional upper limit normal (ULN) * Bilirubin =\< 1.5 x ULN * Transaminases =\< 3 x ULN; for documented liver metastases, transaminases up to 5 x ULN is permitted * No evidence of \>= grade 2 peripheral neuropathy * Patients with reproductive potential must be willing to use an adequate contraceptive method (e.g., abstinence, intrauterine device, oral contraceptives, barrier device with spermicide or surgical sterilization) during treatment and for three months after completing treatment; a negative pregnancy test is required fo…