If you are using wooden skewers, soak them in plenty of water for about 10 minutes if grilling on an indoor grill pan or for 30 minutes if grilling on an outdoor grill to prevent them from burning up.
Place all of the veggies in a large bowl or baking dish. Drizzle with olive oil and season with salt, pepper, and garlic. With your hands, toss to combine well. Stick onion pieces in with the vegetables to coat with the marinade; avoid tossing once onion is added so that the onion does not fall apart.
Alternate the vegetables with the onions on wooden or metal skewers. The onions will get nice and juicy rubbing up against the other veggies. You can do this up to a few hours before you grill them.
Preheat a grill pan over medium-high heat.
Arrange the skewers on the grill pan and cook, turning often, until slightly charred, about 15 minutes. Remove from grill and serve hot or at room temperature.
*Cook's Note: To get skewer-able chunks of onions, cut the onions in half through the core and then cut each half into quarters. Remove 2 or 3 of the innermost layers, leaving the larger outermost layers. They will fit nicely on your skewers.