Radiation Therapy With or Without Combination Chemotherapy or Pazopanib Before Surgery in Treating Patients With Newly Diagnosed Non-rhabdomyosarcoma Soft Tissue Sarcomas That Can Be Removed by Surgery

Inclusion Criteria: * Note: eligible patients must have a body surface area \>= 0.5 m\^2 AND be able to swallow whole tablets * Newly diagnosed and histopathologically confirmed, potentially resectable NRSTS of the extremity and trunk will be eligible for the chemotherapy or non-chemotherapy cohort based on: * Evidence of chemotherapy sensitivity of the histologic sarcoma subtype based on existing evidence from prior clinical trials * Sufficient risk of metastatic disease to warrant chemotherapy based on size and grade and * Medically deemed able or unable to undergo chemotherapy * Notes: an incisional biopsy or core biopsy is preferred; fine needle aspiration biopsy is not acceptable to establish the diagnosis * ELIGIBLE SITES: * Extremities: upper (including shoulder) and lower (including hip) * Trunk: body wall * INELIGIBLE SITES: Head and neck, visceral organs (with the exception of embryonal sarcoma of the liver), retroperitoneum, peritoneum, pelvis within the confines of the bony pelvis * ELIGIBILITY FOR CHEMOTHERAPY COHORT: * Stage T2a/b (\> 5 cm) and grade 2 or 3 AND * One of the following chemosensitive histologies as defined in the World Health Organization (WHO) classification of soft tissue tumors (with some evidence of good response to chemoradiation and of sufficient high risk of metastases, or clear evidence of metastases): * Unclassified soft tissue sarcomas that are too undifferentiated to be placed in a specific pathologic category in the W…