Phase II Study of Oxaliplatin, Irinotecan, and Capecitabine in Advanced Gastric/Gastroesophageal Junction Carcinoma

Inclusion Criteria: * Patients must have histologically or cytologically confirmed gastric adenocarcinoma or adenocarcinoma of the gastroesophageal junction. Patients must have metastatic or inoperable locally advanced disease; GE Junction tumor location should be documented in the patient's medical record chart using the Siewert classification below: * Type I: Adenocarcinoma of the distal esophagus which usually arises from an area with specialized intestinal metaplasia of the esophagus and which may infiltrate the GE junction from above Type II: True carcinoma of the cardia arising from the cardiac epithelium or short segments with intestinal metaplasia at the GE junction Type III: Subcardial gastric carcinoma which infiltrates the GE junction and distal esophagus from below * Patients must have measurable disease, defined as at least one lesion that can be accurately measured in at least one dimension (longest diameter to be recorded) as \>= 20 mm with conventional techniques or as \>= 10 mm with spiral CT scan * No prior chemotherapy for metastatic or recurrent disease is allowed; one course of neoadjuvant chemotherapy and/or adjuvant chemotherapy with or without radiation therapy as primary treatment is acceptable; at least 4 weeks must have elapsed since prior radiation therapy; patients must have been off previous anti-cancer therapy for at least 4 weeks * Life expectancy of \>= 12 weeks * ECOG performance status 0-2 * Hemoglobin \>= 9.5 g/dL * Absolute neutrophil count \>= 1,500/uL * Platelets \>= 100,000/uL * Total bilirubin =\< 1.5 mg/dL * Creatinine =\< 1.5 mg/dL OR creatinine clearance \>= 60 mL/min/1.73 m\^2 for patients with creatinine levels above institutional normal * The effects of oxaliplatin, irinotecan, and capecitabine on the developing human fetus at the recommended therapeutic dose are unknown; for this reason and because these drugs are known to be teratogenic, women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry and for the duration of study participation; should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately * Ability to understand and the willingness to sign a written informed consent document Exclusion Criteria: * Patients who have had chemotherapy or radiotherapy within 4 weeks prior to entering the study or those who have not recovered from adverse events due to agents administered more than 4 weeks earlier * Patients may not be receiving any other investigational agents * Patients with known brain metastases should be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events; patients should have no greater than grade 2 neuropathy * History of allergic reactions attributed to compounds of similar chemical or biologic composition to oxaliplatin, irinotecan and capecitabine * Patients with NYHA classification III or IV heart disease are ineligible * Patients must not have a known hypersensitivity to 5-fluorouracil * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements * Pregnant women are excluded from this study because the study drugs have the potential to cause teratogenic or abortifacient effects; because there is an unknown but potential risk for adverse events in nursing infants secondary to treatment of the mother with the study drugs, breastfeeding should be discontinued if the mother is treated with oxaliplatin, irinotecan or capecitabine * Patients with immune deficiency are at increased risk of lethal infections when treated with marrow-suppressive therapy; therefore, HIV-positive patients receiving combination anti-retroviral therapy are excluded from the study because of possible pharmacokinetic interactions with the study drugs; appropriate studies will be undertaken in patients receiving combination anti-retroviral therapy when indicated * Patients who are unable to take oral medications are not eligible