Irinotecan/Cisplatin, Potentially Curative Surgery With or Without Floxuridine, Followed by Capecitabine for Stomach and Gastro-esophageal Junction (GEJ) Cancers

* Only untreated patients with histologically documented gastric/GEJ adenocarcinoma, clinical American Joint Committee on Cancer (AJCC) stage grouping (11) IB-IV (Mo) by CT scan and laparoscopy/endoscopic ultrasound, are eligible. Excluded are patients in need of urgent surgery for gastro-intestinal obstruction, perforation or hemorrhage. * Both men and women \>= 18 years of age with Eastern Cooperative Oncology Group (ECOG) performance status 0-2, members of any ethnic group and minorities. * Patients without another invasive malignancy, with adequately treated basal cell or squamous cell skin cancer, free for 5 years or more of in-situ cervix cancer or other in-situ cancer. * Since immune deficiency increases the risk of terminal infections when aggravated by bone marrow suppressive therapy, patients must be without active or uncontrolled infection including HIV. * Patients without psychiatric disorders that may interfere with their consent and/or with protocol follow-up. * An adequate bone-marrow reserve (absolute neutrophil count \>= 1,500/ mmL, thrombocytes \>= 100,000 mmL, hemoglobin \>= 9 gm/dL). * Preserved liver and renal function (total serum bilirubin \<2 mg/dL, SGOT/SGPT =\< 3x the upper limit of normal, alkaline phosphatase =\< 3x the upper limit of normal, blood urea nitrogen (BUN) =\< 30 mg/dL, serum creatinine concentration \<1.5 mg/dL and creatinine clearance \>= 50 mL/min) are required. Creatinine clearance should be normalized for 1.73 M\^2 BSA. The prothrombin time, activated partial thromboplastin time, and thrombin time should be within the range of normal values. * Since chemotherapeutic agents to be used are known or suspected to be teratogenic or with other adverse effects, women must not be pregnant or breast-feeding. All females of childbearing potential must have a blood test or urine study within 2 weeks prior to registration to rule out pregnancy. All patients of reproductive age may not participate unless they agree to use an effective medically acceptable contraceptive method. * Patients without diagnosed Gilbert's disease and bilirubin level \>= 2.0 mg/dL, as these patients may have excessive CPT-11 toxicity. * No prior severe reaction to fluoropyrimidine therapy or known hypersensitivity to 5-fluorouracil. Capecitabine (Xeloda) is contraindicated in patients with severe renal impairment, i.e., creatinine clearance below 30 mL/min, determined by Cockcroft-Gault equation shown on page 15 under (i) Renal impairment. In patients with moderate renal impairment (creatinine clearance 30-50 mL/min), which develops during the course of adjuvant treatment with Capecitabine, the drug is decreased to 75% of the starting dose. * Patients should be without any severe concurrent disease, such as cardiac condition not responding to medication, myocardial infarction within the last 12 months, active infection or uncontrolled pulmonary disease, or any other disease which in judgment of the investigator would make the patient inappropriate for entry into this study. * Patients who signed written informed consent.