Whisk together first 7 ingredients, and, if desired, crushed red pepper. Remove and reserve 3/4 cup marinade. Pour remaining marinade into a shallow dish or large zip-top plastic freezer bag; add steak. Cover or seal, and chill 2 hours. Add onion and next 2 ingredients; toss to coat, cover or seal, and chill 20 minutes.
Remove steak and vegetables from marinade, discarding marinade. Thread steak and vegetables, separately, onto 6 to 8 (12-inch) metal skewers.
Grill, covered with grill lid, over medium-high heat (350° to 400°) 10 to 12 minutes or until done. Serve over mixed salad greens with reserved 3/4 cup marinade.