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.
Rinse eggplant, discard stem, and cut crosswise into 3/4-inch-thick rounds. Thread skewers across and through rounds as directed for onions.
Rinse zucchini, trim ends, and cut crosswise into 3/4-inch-thick rounds. Thread on skewers as directed for onions.
Rinse peppers, cut into quarters lengthwise, stem, and seed. Thread thin skewers through center of slices, leaving about 1/4 inch between pieces.
Rinse mushrooms, trim stems flush with caps, and save stems for other uses.
Mix olive oil and tomatoes. Brush mixture onto vegetables.
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.
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.