This phase I trial studies the side effects and best dose of giving pemetrexed disodium and sorafenib tosylate together in treating patients with advanced solid tumors. Pemetrexed disodium and sorafenib tosylate may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Sorafenib tosylate may also stop the growth of solid tumors by blocking blood flow to the tumor. Giving pemetrexed disodium together with sorafenib tosylate may kill more tumor cells.