This randomized phase II/III trial studies how well pazopanib hydrochloride, combination chemotherapy, and radiation therapy work and compares it to radiation therapy alone or in combination with pazopanib hydrochloride or combination chemotherapy in treating patients with newly diagnosed non-rhabdomyosarcoma soft tissue sarcomas that can be removed by surgery. Radiation therapy uses high energy x rays to kill tumor cells. Drugs used in chemotherapy, such as ifosfamide and doxorubicin hydrochloride, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Pazopanib hydrochloride may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. It is not yet known whether radiation therapy works better when given with or without combination chemotherapy and/or pazopanib hydrochloride in treating patients with non-rhabdomyosarcoma soft tissue sarcomas.