Sorafenib Tosylate, Combination Chemotherapy, Radiation Therapy, and Surgery in Treating Patients With High-Risk Stage IIB-IV Soft Tissue Sarcoma

Inclusion Criteria: * Histologically confirmed, soft-tissue sarcoma: excluding rhabdomyosarcoma (pleomorphic rhabdomyosarcoma patients are eligible), Ewing's, primitive neuroectodermal tumor (PNET), osteosarcoma, or gastrointestinal stromal tumor * American Joint Committee on Cancer (AJCC) (7th edition) stage IIb, III, or IV patients planned for resection of the primary tumor * \> 5 cm in greatest dimension * Intermediate or high-grade * Superficial or deep * Sarcoma located on upper (includes shoulder) or lower (includes hip) extremities or on body wall * Intermediate or high-grade: grades 2 or 3 on scale of 1-3 * Left ventricular ejection fraction (LVEF) \>= 50% * Absolute neutrophil count (ANC) \>= 1500/uL * Hemoglobin (Hgb) \>= 9.0 g/dL * Platelets \>= 100,000/uL * Creatinine =\< 1.5 x upper limit of normal (ULN) * Bilirubin =\< 1.5 mg/dL * Aspartate aminotransferase (AST)/alanine aminotransferase (ALT) =\< 1.5 x ULN * 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 or heparin may be allowed to participate; for patients on warfarin, the INR should be measured prior to initiation of sorafenib and monitored at least weekly, or as defined by the local standard of care, until INR is stable * No prior chemotherapy, radiation, or biotherapy * No major surgery within 4 weeks prior to study entry * No contraindications…