Preheat grill to high; lightly oil grates. Insert two 8-inch-long metal or presoaked wooden skewers through onion slices horizontally.
Place prepared skewers and remaining vegetables on one or two rimmed baking sheets. Drizzle with oil; season with salt and pepper. Working in batches if necessary, remove from baking sheets; arrange on grill. Cook, turning occasionally, until lightly browned and tender, 4 to 8 minutes for squash and 8 to 12 minutes for onions and peppers. Remove skewers, and serve.