Whisk vinegar, chili powder, oil, 2 teaspoons salt and garlic powder in a 9-by-13-inch baking dish. Add steak and turn to coat. Cover and marinate in the refrigerator for at least 1 hour and up to 24 hours.
Position rack in upper third of oven; preheat broiler.
Place the steak on a rimmed baking sheet (discard the marinade). Broil 3 to 4 minutes per side for medium. Transfer to a clean cutting board and let rest for 5 minutes. Thinly slice against the grain. Serve the steak wrapped in warm tortillas and topped with the salsa and cheese.