1. Cut onions crosswise in 3/4-inch-thick slices. Run a slender skewer across and through center of each slice to hold rounds flat and secure; put as many slices on skewer as will fit.
2. Rinse eggplant, discard stem, and cut crosswise into 3/4-inch-thick rounds. Thread skewers across and through rounds as directed for onions.
3. Rinse zucchini, trim ends, and cut crosswise into 3/4-inch-thick rounds. Thread on skewers as directed for onions.
4. Rinse peppers, cut into quarters lengthwise, stem, and seed. Thread thin skewers through center of slices, leaving about 1/4 inch between pieces.
5. Rinse mushrooms, trim stems flush with caps, and save stems for other uses.
6. Mix olive oil and tomatoes. Brush mixture onto vegetables.
7. Set vegetables on a barbecue grill over a solid bed of hot coals or high heat on a gas grill (you can hold your hand at grill level only 2 to 3 seconds). Close lid on gas grill. Cook, turning as needed, until vegetables are browned and tender when pierced, 8 to 10 minutes. Transfer to a platter as cooked.
8. Slice mushrooms. Remove vegetables from skewers. Add mushrooms to platter and season vegetables to taste with salt and pepper. Serve hot or at room temperature.