Preoperative Thalidomide With Radiation Therapy For Patients With Low-Grade Primary Soft Tissue Sarcoma or Thalidomide With Radiation Therapy and Chemotherapy For Patients With High-Grade or Intermediate-Grade Primary Soft Tissue Sarcoma of the Arm, Leg, or Body Wall

Inclusion Criteria: * Diagnosis of primary soft tissue sarcoma * T2a or T2b disease * Superficial or deep tumor * Grade 1, 2, 3, or 4 * Tumor located on the upper extremity (including shoulder), lower extremity (including hip), or trunk * Meets 1 of the following criteria: * Tumor ? 8 cm in maximal diameter and grade 3 or 4 (intermediate or high grade) (cohort A) * Tumor \> 5 cm in maximal diameter and grade 1 or 2 (low grade) (cohort B) * Locally recurrent disease allowed provided there has been no prior radiotherapy to the primary tumor * No histologically confirmed rhabdomyosarcoma, extraosseous Ewing's primitive neuroectodermal tumors, osteosarcoma or chondrosarcoma, Kaposi's sarcoma, angiosarcoma, desmoid tumors, or dermatofibrosarcoma protuberans * No overt evidence of lung metastases (CT scan evidence of small incidental lesions without histologic diagnosis allowed) * No evidence of other metastases * No sarcoma of the head, neck, intra-abdominal, or retroperitoneal region * Performance status - Zubrod 0-1 * At least 2 years * Absolute neutrophil count ? 1,500/mm\^3 * Platelet count ? 120,000/mm\^3 * Hemoglobin ? 8.0 g/dL (cohort A) * No known hypercoagulable disorders, such as the following: * APC resistance (factor V Leiden) * Protein S deficiency * Protein C deficiency * Antithrombin III deficiency * Hyperhomocystinemia * Dysplasminogenemia * High plasminogen activator inhibitor * Dysfibrinogenemia * Antiphospholipid syndrome * Th…