Sorafenib Tosylate and Hypoxia-Activated Prodrug TH-302 in Treating Patients With Advanced Kidney Cancer or Liver Cancer That Cannot Be Removed By Surgery

Phase I Registration - Inclusion Criteria * Age ≥18 years * Cytological or histological confirmed diagnosis of advanced hepatocellular or renal cell carcinoma. HCC patients should not be amenable to treatment with surgery or to orthotopic liver transplant. * Patients must have measurable disease as defined in the protocol. * RCC patients only: Tumor progression after receiving standard/approved chemotherapy and/or targeted agent, where there is no approved therapy or for tumors where sorafenib based therapy would be standard therapy. * HCC patients only: * First line (i.e., no prior systemic therapy) or second line (with prior first line sorafenib therapy only) advanced HCC. * Child Pugh class A or B7 liver disease * Prior chemoembolization, radioembolization, radiofrequency ablation (RFA), or other local ablative therapies are permissible if ≥6 weeks from procedure with evidence of progression or new metastatic disease, if applicable. * ECOG Performance Status (PS) 0 or 1. * The following laboratory values obtained ≤14 days prior to registration. * Absolute neutrophil count (ANC) ≥1200/mm3 * Peripheral Platelet Count (PLT) ≥75,000/mm3 * Hemoglobin (HgB) \>8.5 g/dL * Bilirubin ≤3.0 x upper limit of normal (ULN) * SGOT (AST) ≤2.5 x ULN, if subject has HCC or liver metastases ≤5 x UL * SGPT (ALT) ≤2.5 x ULN, if subject has HCC or liver metastases ≤5 x ULN * Creatinine ≤1.5 x ULN * INR ≤1.5 x ULN. Patients receiving anti-coagulation therapy are permitted as long as they have a stable INR≤3.0. * Negative pregnancy test done ≤7 days prior to registration, for women of childbearing potential only. * Provide informed written consent. * Willing to return to Alliance enrolling institution for follow-up. * Life expectancy ≥3 months. Phase I Registration - Exclusion Criteria * Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown. * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception for the duration of study participation. Men and women should continue to use adequate birth control after the last administration of sorafenib and TH-302 under the guidance of their treating physician. * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens. * Receiving any other investigational agent. * Other active malignancy ≤3 years prior to registration. EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix. NOTE: If there is a history or prior malignancy, they must not be receiving other specific treatment (other than hormonal therapy) for their cancer. * Inadequately controlled hypertension (systolic blood pressure of \>150 mmHg or diastolic pressure \>100 mmHg on anti-hypertensive medications). * Major surgical procedures, or significant traumatic injury ≤14 days prior to registration or anticipation of need for elective or planned major surgical procedure during the course of the study. * New York Heart Association (NYHA) classification III or IV congestive heart failure. * Received treatment with radiation therapy or investigational therapy ≤28 days prior to registration. * RCC patients only: Having received chemotherapy prior to study entry within 5 half-lives of the agent (as described in the package insert), or 4 weeks prior to registration (whichever is shorter) with resolution of side effects from therapy to ≤grade 1. * Known central nervous system or brain metastasis that are either symptomatic or untreated. Note: Patients with neurological symptoms must undergo a CT scan/MRI of the brain to exclude brain metastasis. * Note: Subjects with CNS metastases that have been treated and are stable without symptoms for ≥ 4 weeks after completion of treatment are eligible. * HCC patients only: Cancer potentially amenable to local modalities of therapy or surgical resection. * Known or suspected allergy or hypersensitivity to any component of TH-302, sorafenib, or any of the sorafenib excipients. * Any condition that severely impairs patient's ability to swallow whole pills. * QTc interval \>500 msec on baseline EKG. * Documented history of prolonged QTc interval ≤ 6 months prior to registration. * Receiving any medication that has documented data or is generally accepted as having increased risk of QT prolongation and/or Torsades de Pointes. * Receiving any medications or substances that are inducers or strong or moderate inhibitors of CYP3A4, see the protocol for a complete listing. * Fibrolamellar histology HCC, mixed hepatocholangiocarcinoma, hepatic sarcomas and other non-HCC primary liver tumors. * History of lobectomy involving \>50% of lobe. * Radioembolization within 8 weeks of Day 1 dosing of sorafenib. Phase II Registration - Inclusion Criteria * Age ≥18 years * Cytological or histological confirmed diagnosis of hepatocellular carcinoma that is locally advanced or metastatic and is not amenable to treatment with surgery or to orthotopic liver transplant. * Patients must have measurable disease as defined in Section 11.0 must have at least one non-nodal lesion. * First line advanced HCC (i.e., no prior systemic therapy). * Child Pugh class A or B7 liver disease * Prior chemoembolization, radioembolization, radiofrequency ablation (RFA), or other local ablative therapies are permissible if ≥6 weeks from procedure with evidence of progression or new metastatic disease, if applicable. * ECOG Performance Status (PS) 0 or 1. * The following laboratory values obtained ≤14 days prior to registration. * Absolute neutrophil count (ANC) ≥1200/mm\^3 * Peripheral Platelet Count (PLT) ≥75,000/mm\^3 * Hemoglobin (HgB) \>8.5 g/dL * Total bilirubin ≤3.0 x upper limit of normal (ULN) * SGOT (AST) ≤5 x ULN. * SGPT (ALT) ≤5 x ULN. * Creatinine ≤1.5 x ULN. * INR ≤1.5 x ULN. Patients receiving anti-coagulation therapy are permitted as long as they have a stable INR≤3.0. * Negative pregnancy test done ≤7 days prior to registration, for women of childbearing potential only. * Provide informed written consent. * Willing to return to Alliance enrolling institution for follow-up. * Life expectancy ≥3 months. * Ability to receive intravenous contrast for the purpose of imaging. Phase II Registration - Exclusion Criteria * Any of the following because this study involves an investigational agent whose genotoxic, mutagenic and teratogenic effects on the developing fetus and newborn are unknown. * Pregnant women * Nursing women * Men or women of childbearing potential who are unwilling to employ adequate contraception for the duration of study participation. Men and women should continue to use adequate birth control after the last administration of sorafenib and TH-302 under the guidance of their treating physician. * Co-morbid systemic illnesses or other severe concurrent disease which, in the judgment of the investigator, would make the patient inappropriate for entry into this study or interfere significantly with the proper assessment of safety and toxicity of the prescribed regimens. * Receiving any other investigational agent. * Other active malignancy ≤3 years prior to registration. EXCEPTIONS: Non-melanotic skin cancer or carcinoma-in-situ of the cervix. NOTE: If there is a history or prior malignancy, they must not be receiving other specific treatment (other than hormonal therapy) for their cancer. * Inadequately controlled hypertension (systolic blood pressure of \>150 mmHg or diastolic pressure \>100 mmHg on anti-hypertensive medications). * Major surgical procedures, or significant traumatic injury ≤14 days prior to registration or anticipation of need for elective or planned major surgical procedure during the course of the study. * New York Heart Association (NYHA) classification III or IV congestive heart failure. * Received treatment with radiation therapy or investigational therapy ≤28 days prior to registration. * Known central nervous system or brain metastasis that are either symptomatic or untreated. Note: Patients with neurological symptoms must undergo a CT scan/MRI of the brain to exclude brain metastasis. * Note: Subjects with CNS metastases that have been treated and are stable without symptoms for ≥ 4 weeks after completion of treatment are eligible. * Fibrolamellar histology HCC, mixed hepatocholangiocarcinoma, hepatic sarcomas and other non-HCC primary liver tumors. * Cancer potentially amenable to local modalities of therapy or surgical resection. * Known or suspected allergy or hypersensitivity to any component of TH-302, sorafenib, or any of the sorafenib excipients * Any condition that severely impairs patient's ability to swallow whole pills. * QTc interval \>500 msec on baseline EKG. * Documented history of prolonged QTc interval ≤ 6 months prior to registration. * Receiving any medication that has documented data or is generally accepted as having increased risk of QT prolongation and/or Torsades de Pointes. * Receiving any medications or substances that are inducers or strong or moderate inhibitors of CYP3A4, please see protocol for a complete listing. * History of lobectomy involving \>50% of lobe. * Radioembolization within 8 weeks of Day 1 dosing of sorafenib.