In a small bowl, whisk the first six ingredients. Pour 1/3 cup into a large resealable plastic bag; add steak. Seal bag and turn to coat; refrigerate for 3 hours. Cover and refrigerate remaining marinade for dressing.
Drain and discard marinade from steak. Grill, covered, over indirect medium heat for 11-12 minutes on each side or until meat reaches desired doneness (for medium-rare, a meat thermometer should read 145°; medium, 160°; well-done, 170°). Cut across the grain into thin slices.
In a large serving bowl, combine the greens, tomato, radishes, celery, onions and beef. Drizzle with reserved marinade; toss to coat. Yield: 4 servings.