Sorafenib Tosylate in Treating Younger Patients With Relapsed or Refractory Rhabdomyosarcoma, Wilms Tumor, Liver Cancer, or Thyroid Cancer

Inclusion Criteria: * Patients must have had histologic verification of one of the malignancies listed below at original diagnosis or at relapse: * Rhabdomyosarcoma (RMS) * Wilms tumor * Hepatocellular carcinoma (HCC) * Papillary thyroid carcinoma (PTC) * Patients must have relapsed or refractory disease (RMS, Wilms tumor, HCC, PTC) * Patients must have radiographically measurable disease; measurable disease is defined as the presence of at least one lesion on magnetic resonance imaging (MRI) or computed tomography (CT) scan that can be accurately measured with the longest diameter a minimum of 10 mm in at least one dimension (CT scan slice thickness no greater than 5 mm) * The following do not qualify as measurable disease: * Malignant fluid collections (e.g., ascites, pleural effusions) * Bone marrow infiltration * Lesions only detected by nuclear medicine studies (e.g., bone, gallium, or positron emission tomography \[PET\] scans) * Elevated tumor markers in plasma or cerebrospinal fluid(CSF) * Previously radiated lesions that have not demonstrated clear progression post radiation * Leptomeningeal lesions that do not meet the requirements noted above * Patients with HCC must be relapsed or refractory to conventional chemotherapy * Patients with PTC must be refractory to radioactive iodine (RAI) * Patient's current disease state must be one for which there is no known curative therapy or therapy proven to prolong surviv…