Special equipment: Metal skewers or a grill basket
Prepare grill for cooking.
Thread onions onto skewers (or put in grill basket), then brush with 1 tablespoon oil and season with salt and pepper. When fire is medium-hot (you can hold your hand 5 inches above rack for 3 to 4 seconds), grill onions, turning occasionally, until tender, 16 to 20 minutes. Transfer to a cutting board. When just cool enough to handle, cut onions into 1-inch pieces and toss with vinegar in a bowl. Season with salt and pepper. While onions are grilling, stir together the lime juice and remaining 3 tablespoons oil in a shallow dish, then add steak and marinate at room temperature, turning once, 10 minutes.
Pat steak dry, then rub with chili powder, cumin, and coriander and season with salt and pepper. Grill steak on lightly oiled grill rack, turning once, 6 to 10 minutes total for medium-rare. Transfer to cutting board, then let stand 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.
If using fresh tomatillos, remove husks and rinse under warm water to remove stickiness. If using canned tomatillos, drain and measure out 4 cups. Broil fresh tomatillos (do not broil canned), chiles, garlic, and onions on rack of a broiler pan 1 to 2 inches from heat, turning once, until softened and slightly charred, about 8 minutes.
Peel garlic and pull off tops of chiles. Puree all ingredients in a food processor.
Yield: 6 cups
If you aren't able to grill, onions (no need to skewer) and steak can be cooked in a lightly oiled well-seasoned ridged grill pan over moderately high heat and tortillas can be toasted over gas (hold with tongs) or directly on top of electric burners. Cut skirt steak into pieces to fit in grill pan and grill in batches without crowding. Salsa can be made 1 day ahead and chilled, covered.