Heat vegetable oil in a large Dutch oven over medium-high heat. Add the squash and onion, and sauté 5 minutes. Add 1 cup water and the next 4 ingredients (1 cup water through chile); cover and cook 5 minutes. Add 1 1/2 cups water, salt, and tomatoes; cover, reduce heat, and simmer 20 minutes. Add the corn and beans; cover and cook 15 minutes. Discard the chile.