Marinate the steaks. In a small bowl, mix the oil, lime juice and salt. Place the steaks in a non-reactive dish — a 13-by-9 glass baking dish works well — and pour the marinade over the meat. Cover with plastic wrap and refrigerate for about 1 hour.
Prepare the nopales. Holding a paddle with a pair of tongs, trim off the edge that outlines the paddle, including the blunt end where the paddle was severed from the plant. Slice or scrape off the spiny nodes from both sides of the paddle.
Heat a gas grill (or grill pan) to medium or light a charcoal fire and let it burn until medium hot.
Spray or brush the cleaned paddles and onions with oil and season with salt. Place them on the grill, cooking until completely caramelized, about 8 to 10 minutes, then slice into strips.
Place steak on the grill and cook for about 8 minutes per side, then let it rest on a cooling rack atop a sheet tray for about 5 minutes. Working against the grain, slice the steak into 1/2-inch strips.
Place steak on a platter with the cactus, onion, lime wedges, warm tortillas and your favorite red salsa. Dinner is ready.