Short-Course Chemoradiotherapy Followed by Chemotherapy for the Treatment of Resectable Gastric Adenocarcinoma

Inclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) performance status =\< 2 * Patients with a biopsy-confirmed diagnosis of adenocarcinoma of the stomach * No evidence of distant metastatic disease based on standard of care preoperative imaging evaluation * Evidence of T2 stage or greater primary tumor, or any T stage with node positive disease based on endoscopic ultrasound or standard of care imaging * Leukocytes \>= 3,000/ul * Absolute neutrophil count \>= 1,500/ul * Platelets \>= 60,000/UI * Glomerular filtration rate \>= 60 mL/min/1.73 m\^2. The estimated glomerular filtration rate (eGFR) is calculated using the Chronic Kidney Disease Epidemiology Collaboration (CKD-EPI) equation. The eGFR declines with age. eGFR \< 60 mL/min/1.73 m2 is considered as "decreased". This equation should only be used for patients 18 and older. According to the National Kidney Foundation's Kidney Disease Outcome Quality Initiative (KDOQI) classification and 2012 Kidney Disease Improving Global Outcomes (KDIGO) Clinical Practice Guideline, the stage of CKD should be categorized based on estimated GFR Exclusion Criteria: * Presence of metastatic disease on staging with standard of care imaging, with or without diagnostic laparoscopy. Subjects not able to undergo staging laparoscopy due to previous surgery will not be excluded from this trial, and the determination of absence of metastatic disease will be decided solely on imaging consistent with our current standard of care * Patients with known malabsorption syndromes or a lack of physical integrity of the upper gastrointestinal tract * Infections such as pneumonia or wound infections that would preclude protocol therapy * Women with a positive urine or serum pregnancy test are excluded from this study; women of childbearing potential (defined as those who have not undergone a hysterectomy or who have not been postmenopausal for at least 12 consecutive months) must agree to refrain from breast-feeding and practice adequate contraception as specified in the informed consent. Adequate contraception consists of oral contraceptive, implantable contraceptives, injectable contraceptives, barrier methods, or abstinence. Contraception for males consists of barrier methods or abstinence * Subjects with unstable angina or New York Heart Association grade II or greater congestive heart failure * Subjects deemed unable to comply with study and/or follow-up procedures * Subjects with a known hypersensitivity to protocol systemic chemotherapy that was life threatening, required hospitalization or prolongation of existing hospitalization, or resulted in persistent or significant disability or incapacity * Prior radiotherapy to the same field * Comorbid conditions (examples - collagen vascular diseases, certain genetic conditions that predispose to secondary malignancies) that are prohibitive to preoperative therapy, or contraindications to radiotherapy