In a large saucepan, sauté peppers and onion in oil until crisp-tender. Add garlic; cook 1 minute longer. Drain. Stir in the tomato sauce, tomato paste, water, sugar, basil, salt, and oregano. Bring to a boil. Reduce heat; cover and simmer for 30 minutes or until heated through.
Meanwhile, grill sausages, covered, over medium heat for 10-16 minutes or until a thermometer reads 160°, turning occasionally. Serve on buns with sauce and cheese if desired.