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 to medium-high or light a charcoal fire and let it burn until the charcoal is covered with white ash. Lay the nopales and onions on the grill and drizzle with oil. Add the tomatoes and chiles to the grill and cook, turning everything at least once, until the vegetables are charred on all sides and very soft, about 10 minutes for the nopales and 15 minutes for the onions, tomatoes and chiles. Cool, then peel the chiles and tomatoes, if you wish. Stem and seed the chiles, then cut them into 1/2-inch pieces and scoop into a bowl. Chop the tomatoes and nopales the same size and add to the bowl. Using only the white part of the onion, slice them 1/4-inch thick and add to the bowl. Sprinkle in the oregano and mix well. Taste and season with salt, usually a generous teaspoon and your salsa is ready to serve.