In a small bowl, combine olive oil, balsamic vinegar, garlic, salt, black pepper and oregano.
Snap off and discard woody bases from asparagus. If desired, scrape off scales. Brush mushrooms and all vegetables with oil mixture, reserving the remaining oil mixture.
Place mushrooms on the rack of an uncovered grill directly over medium hot coals. Grill for 8 to 10 minutes or until tender, turning once and brushing with reserved oil mixture. Add vegetables to grill. Grill for 3 to 4 minutes or until tender, turning once and brushing with reserved oil mixture. Discard any remaining mixture.
To serve, slice mushrooms. Arrange mushroom slices and other vegetables on a serving plate.