This phase II clinical trial studies how well combining different regimens of chemotherapy and gefitinib with radiation therapy work in treating patients with stage III non-small cell lung cancer. 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. Biological therapies such as gefitinib may interfere with the growth of tumor cells and slow the growth of non-small cell lung cancer. Radiation therapy uses high-energy x-rays to damage tumor cells. Giving different regimens of combination therapy together with gefitinib and radiation therapy may be an effective treatment for non-small cell lung cancer.