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 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.
Fry the tortillas in a oil 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. Add as much cheese as you like. Garnish with lime wedges, and serve.