This pilot clinical trial studies the safety and effectiveness of continuous hepatic arterial infusion (HAI) of floxuridine (FUDR) alone or in combination with other chemotherapeutic drugs in treating patients with locally advanced cholangiocarcinoma that cannot be removed by surgery. HAI is a method to deliver higher concentrations of FUDR more directly to liver tumors and reduces side effects. HAI alone or in combination with oxaliplatin and/or gemcitabine may significantly improve clinical outcomes of patients with locally advanced cholangiocarcinoma.