This randomized phase III trial is studying combination chemotherapy followed by surgery and two different combination chemotherapy regimens with or without PEG-interferon alfa-2b to compare how well they work in treating patients with osteosarcoma. Drugs used in chemotherapy work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving more than one drug (combination chemotherapy) may kill more tumor cells. Biological therapies, such as PEG-interferon alfa-2b, may interfere with the growth of tumor cells. Giving combination chemotherapy before surgery may shrink the tumor so it can be removed. Giving combination chemotherapy together with PEG-interferon alfa-2b after surgery may kill any remaining tumor cells. It is not yet known whether giving combination therapy together with PEG-interferon alfa-2b is more effective than two different combination chemotherapy regimens alone after surgery in treating osteosarcoma.