A Study of Combination of Gemcitabine, Oxaliplatin (GEMOX)-Sorafenib in Patients With Advanced Biliary Tract Cancer

Inclusion Criteria: * Age \>= 18 years * Histologically or cytologically confirmed biliary tract or gallbladder carcinoma * Any stage of disease is allowed but the patients must not be candidates for curative resection * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0-1 in Ph I * ECOG performance status 0-2 in Ph II. Patients with ECOG PS of 2 will only be enrolled if they will comprise at most 25% of the total accruals. This will be monitored in real time to ensure that at any point during accrual, PS 2 patients will comprise \<= 25% of the total accruals * Patients must have normal organ and marrow function as defined below within 14 days of study entry: * Absolute neutrophil count \>= 1,500 cells/mm3 * Platelet count \>= 60,000/mm3 * Creatinine \< 1.5 upper limit of normal (ULN). * Aspartate transaminase (AST) and Alanine transaminase (ALT) \<= 2.5 x ULN. * Bilirubin \<= 3.0 mg/dl * International normalized ratio (INR) \< 1.5 or a prothrombin time (PT)/partial thromboplastin time (PTT) within normal limits. Patients receiving anti-coagulation treatment with an agent such as warfarin will not be candidates for the trial. Patients on anticoagulation with low molecular weight or heparinoids are protocol candidates. * Any number of previous lines of chemotherapy is allowed for the phase I portion * During the phase II trial, no prior chemotherapy for inoperable or metastatic disease is allowed except 5-FU or Capecitabine as radiosensitizers. Prior adjuvant chemotherapy is allowed. * Women of childbearing potential must have a negative serum pregnancy test performed within 7 days prior to the start of treatment * Women of childbearing potential and men must agree to use adequate contraception (barrier method of birth control) prior to study entry and for the duration of study participation. Men should use adequate birth control for at least three months after the last administration of sorafenib. * Ability to understand and the willingness to sign a written informed consent. A signed informed consent must be obtained prior to any study specific procedures. * Life expectancy of greater than 12 weeks Exclusion Criteria: * Investigational agents within 28 days prior to Day 1 of study * Chemotherapy within 4 weeks prior to Day 1 of study * Nitrosoureas, mitomycin-C within 6 weeks prior to Day 1 of study. * Prior treatment with sorafenib, gemcitabine or oxaliplatin * Prior history of peripheral neuropathy \> Grade 1 (e.g., diabetic neuropathy) * Pregnant or breast-feeding female * Patients with a history of allergic reactions or sensitivity attributed to compounds of similar chemical or biologic composition to sorafenib, oxaliplatin or gemcitabine * Patients with GI tract disease resulting in an inability to take oral medication, malabsorption syndrome, a requirement for IV alimentation, prior surgical procedures affecting absorption, uncontrolled inflammatory GI disease (e.g., Crohn's, ulcerative colitis) * Cardiac disease: Congestive heart failure \> class II New York Heart Association (NYHA). Patients must not have unstable angina (anginal symptoms at rest) or new onset angina (began within the last 3 months) or myocardial infarction within the past 6 months. * Cardiac ventricular arrhythmias requiring anti-arrhythmic therapy. * Uncontrolled hypertension defined as systolic blood pressure \> 150 mmHg or diastolic pressure \> 90 mmHg, despite optimal medical management. * Known brain metastasis. Patients with neurological symptoms must undergo a CT scan/MRI of the brain to exclude brain metastasis. * Known human immunodeficiency virus (HIV) infection and Hepatitis B and Hepatitis C. * Active clinically serious infection \> CTCAE Grade 2. * Arterial thrombotic/embolic events like myocardial infarct and cerebrovascular accident including transient ischemic attacks within the past 6 months. * Pulmonary hemorrhage/bleeding event \> CTCAE Grade 2 within 4 weeks of first dose of study drug. * Any other hemorrhage/bleeding event \> CTCAE Grade 3 within 4 weeks of first dose of study drug. * Serious non-healing wound, ulcer, or bone fracture. * Evidence or history of bleeding diathesis or coagulopathy * Major surgery, open biopsy or significant traumatic injury within 4 weeks of first study drug. * Use of St. John's Wort or rifampin (rifampicin). * Any medical condition, which in the opinion of the investigator places the patient at an unacceptably high risk for toxicities