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 * Thrombocythemia * Dysproteinemia * Fibrin split products \< 2 times upper limit of normal (ULN) * Fibrinogen \> 200 mg/dL * Bilirubin ? 1.5 mg/dL (1.0 mg/dL for patients with Gilbert's syndrome) * AST and ALT ? 2.0 times ULN * PT and PTT \< 1.25 times ULN (except in patients treated with anticoagulants for unrelated medical conditions \[e.g., atrial fibrillation\]) * No history of hepatic cirrhosis * Creatinine ? 1.5 mg/dL * Creatinine clearance \> 60 mL/min * No atherosclerotic coronary artery disease that required bypass surgery within the past year * No uncompensated coronary artery disease by ECG or physical examination * No myocardial infarction within the past 6 months * No severe or unstable angina within the past 6 months * No uncompensated congestive heart failure * No New York Heart Association class II-IV heart disease * No symptomatic peripheral vascular disease * No history of deep vein thrombosis * Cohort A only: * EF ? 50% within the past 6 months * LVEF \> 50% * No pulmonary embolus except if caused directly by foreign body implants (e.g., central venous catheters or portacaths) * No global neurocognitive symptomatology * No fatigue ? grade 2 * No history of uncontrolled seizures or uncontrolled seizure disorder * No sensory neuropathy ? grade 2 except for localized neuropathy due to mechanical cause or trauma * No other malignancies within the past 3 years except non-invasive malignancies (e.g., carcinoma in situ of the cervix, breast, or oral cavity) or squamous or basal cell skin cancer * No history of uncontrolled myxedema * No hypothyroidism ? grade 3 * No active uncontrolled bacterial, viral, or fungal infection * No other significant illness that would preclude surgery * No other major illness or psychiatric impairment that would preclude study therapy * No known AIDS * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use 2 effective barrier methods of contraception for 4 weeks before, during, and for at least 4 weeks after study treatment * No prior thalidomide * No prior biologic therapy for this tumor * No prior chemotherapy for this tumor * See Disease Characteristics * No prior radiotherapy for this tumor * See Cardiovascular * No other concurrent investigational drugs * No concurrent sedating drugs * No concurrent illegal sedating "recreational" drugs * No concurrent alcohol intake of more than 1 drink per day