This phase III trial compares the effect of modified fluorouracil, leucovorin calcium, oxaliplatin, and irinotecan (mFOLFIRINOX) to modified fluorouracil, leucovorin calcium, and oxaliplatin (mFOLFOX) for the treatment of advanced, unresectable, or metastatic HER2 negative esophageal, gastroesophageal junction, and gastric adenocarcinoma. The usual approach for patients is treatment with FOLFOX chemotherapy. Chemotherapy drugs work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Fluorouracil stops cells from making DNA and it may kill tumor cells. Leucovorin is used with fluorouracil to enhance the effects of the drug. Oxaliplatin works by killing, stopping, or slowing the growth of tumor cells. Some patients also receive an immunotherapy drug, nivolumab, in addition to FOLFOX chemotherapy. Immunotherapy may induce changes in body's immune system and may interfere with the ability of tumor cells to grow and spread. Irinotecan blocks certain enzymes needed for cell division and DNA repair, and it may kill tumor cells. Adding irinotecan to the FOLFOX regimen could shrink the cancer and extend the life of patients with advanced gastroesophageal cancers.

This trial studies how well proton beam radiation therapy compared with intensity modulated photon radiotherapy works in treating patients with stage I-IVA esophageal cancer. Proton beam radiation therapy uses a beam of protons (rather than x-rays) to send radiation inside the body to the tumor without damaging much of the healthy tissue around it. Intensity modulated photon radiotherapy uses high-energy x-rays to deliver radiation directly to the tumor without damaging much of the healthy tissue around it. It is not yet known whether proton beam therapy or intensity modulated photon radiotherapy will work better in treating patients with esophageal cancer.