Stir together lime juice and 1 teaspoon of salt and 2 tablespoons of oil in a shallow dish. Add steak and marinate in refrigerator, turning once, for 4 to 6 hours.
Prepare grill, grill pan or broiler for cooking. Thread onions onto skewers or put in a grill basket. Brush with 1/2 tablespoon oil, and season with salt and pepper. When fire is medium-hot (to test: you should be able to hold your hand 5" above rack for 3 to 4 seconds), grill onions. Turn onions occasionally, until tender and caramelized, about 16 to 20 minutes. Transfer to a cutting board. When just cool enough to handle, cut onions into 1" pieces and toss with vinegar and 1/2 teaspoon salt.
Pat steak dry, and rub with pepper. Grill steak on lightly oiled grill rack, turning once, for 6 to 10 minutes total for medium-rare. Transfer to cutting board. Let stand for 5 minutes before cutting diagonally into thin slices.
While steak is standing, toast tortillas directly on grill rack, turning once, until puffed slightly and browned in spots, about 1 minute total. Serve steak, onions, cilantro and salsa all wrapped in tortillas. Serve with lime wedges. Note to cook without a grill: Onions (no skewer) and steak can be cooked in a lightly oiled, well-seasoned grill pan over moderately high heat and tortillas can be toasted over gas burner (hold with tongs) or directly on top of electric burners. Cut steak into pieces to fit in grill pan and grill in batches without crowding.