This phase II trial studies how well giving irinotecan hydrochloride together with oxaliplatin and capecitabine works as first-line therapy in treating patients with metastatic or unresectable locally advanced small bowel cancer. Drugs used in chemotherapy, such as irinotecan hydrochloride, oxaliplatin, and capecitabine, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving more than one drug (combination chemotherapy) may kill more tumor cells.