Lightly brush vegetables with the vegetable oil. Using a charcoal grill, place vegetables on the rack of the grill over medium-hot coals. Cover and grill for 3 to 5 minutes for asparagus, turning once, and about 10 minutes for the zucchini, bell peppers, and onion, turning once, or until vegetables are tender. Remove and cool slightly. (For a gas grill, preheat grill. Reduce heat to medium-high. Add vegetables to grill rack and grill as above.)