1. Preheat grill to 350° to 400° (medium-high) heat. Whisk together first 4 ingredients in a large shallow dish or zip-top plastic freezer bag; add beef, turning to coat. Cover or seal bag, and chill 20 minutes, turning once.
2. Meanwhile, soak the wooden skewers in water 10 minutes.
3. Remove beef from marinade, discarding marinade. Thread beef onto 4 skewers, onion onto 2 skewers, and mushrooms and peppers onto remaining 2 skewers. Sprinkle kabobs with desired amount of salt and pepper.
4. Grill beef and vegetables at the same time, covered with grill lid. Grill beef 6 minutes on each side or to desired degree of doneness. Grill vegetables 10 minutes or until tender, turning occasionally.