Lay the flank steak in a large glass baking dish. In a medium bowl, whisk together the vinegar, soy sauce, 4 cloves of garlic, juice of two limes, and olive oil. Season with salt, black pepper, white pepper, garlic powder, chili powder, oregano, cumin and paprika. Whisk until well blended, then pour over the steak in the dish. Turn over once to coat both sides. Cover with plastic wrap, and marinate for 1 to 8 hours.
In a small bowl, stir together 1 chopped white onion, cilantro, and the juice of 1 lime. Set aside to use as a relish for the tacos.
Heat a skillet over medium-high heat. Toast chile pods in the skillet for a few minutes, then remove to a bowl of water to soak for about 30 minutes. Preheat the oven to 450 degrees F (230 degrees C).
Place the tomatoes, 1 onion, jalapenos, and 4 cloves of garlic onto a baking sheet. Roast in the oven for about 20 minutes, until toasted but not burnt. Place the roasted vegetables, and soaked chile pods into a blender or food processor, along with salt and pepper. Puree until smooth.
Heat vegetable oil in a large skillet over medium-high heat. Cut the marinated flank steak into cubes or strips. Cook, stirring constantly, until the meat is cooked through and most of the liquid has evaporated.
Warm the tortillas in a skillet for about a minute on each side to make them pliable. Tortillas may also be warmed in a microwave oven. Arrange two or three tortillas on a plate, and lay a generous amount of beef over them. Top with a sprinkle of the onion relish and a large spoonful of the pureed salsa. Add as much cheese as you like. Garnish with lime wedges, and serve.