Heat gas or charcoal grill. In 5-quart Dutch oven, cook pasta as directed on package. Drain and return to Dutch oven; cover to keep warm. In large bowl, toss tomatoes, oregano and garlic. In small bowl, mix oil, vinegar, sugar, salt and pepper. Add to tomato mixture; mix well. Set aside.
Place bell peppers, zucchini and onion on ungreased cookie sheet. Spray vegetables with cooking spray. Lightly sprinkle with salt, if desired. Place vegetables directly on grill over medium heat. Cook uncovered 8 to 14 minutes, turning frequently. Remove vegetables from grill as they become crisp-tender. Coarsely chop vegetables. Add to tomato mixture; mix well. Add mixture to pasta in Dutch oven; toss gently. Spoon into serving bowl; sprinkle with cheese.