Combine first 6 ingredients in a small bowl, stirring with a whisk until blended.
Combine steak, mushrooms, and onion in a large zip-top plastic bag.
Add 1/2 cup vinegar mixture to bag; seal. Marinate in refrigerator 2 1/2 hours, turning occasionally. Reserve remaining 6 tablespoons vinegar mixture.
. Prepare grill.
Remove steak and onion from bag, and place on grill rack coated with cooking spray. Grill 6 to 8 minutes on each side or until steak is desired degree of doneness and onion is tender.
Remove mushrooms from bag; discard marinade.
Place mushrooms on grill rack; grill 4 to 5 minutes on each side or until tender.
Cut mushrooms into 1/2-inch-thick slices.
Let steak stand 5 minutes.
Cut steak diagonally across grain into thin slices.
. Chop onion; combine onion and mushrooms in a medium bowl.
Combine mixed greens and tomatoes, and arrange evenly on plates. Top evenly with mushroom mixture. Arrange steak evenly over mushroom mixture; drizzle each serving evenly with reserved vinegar mixture.