Preheat the oven to 350°F (180°C).
Mix ½ teaspoon salt, ¼ teaspoon black pepper, ½ teaspoon ground cumin, ¼ teaspoon chili powder, ¼ teaspoon ground corianderand ¼ teaspoon dried oregano in a small bowl. Coat each piece of 1 ½ pounds pork shoulder on all sides.
Heat 2 tablespoons of cooking oil in a frying pan or skillet and brown the pork at high temperature on all sides for about 2 minutes, or until it's seared outside (crisp crust) while the meat remains raw inside.
Transfer the pork to a roasting pan where the pork pieces fit snugly. Add 3 garlic cloves halved in between.
Squeeze 1 orange and pour the orange juice over the meat. Cut the remaining 1 orange into pieces and scatter them around the pork. Add a little more water to barely cover the pork.
Cover the pan with foil and roast in the oven for about 2 hours, turning it around a few times. If after 2 hours the pork shoulder is not as soft as you want it to be (it will depend on how large the pieces are), you can cook it more.
Remove from the oven, remove the foil and transfer the pork to a plate, reserving the pan juices. Using two forks, shred the pork pieces right there in the pan. Transfer the juices to a saucer or jar.
Lightly fry 6 corn tortillas on both sides, brushing them a little with the roasting juices.
Place 3-4 tablespoons of pulled pork on half of the tortilla and moisten with some of the remaining roasting juices. Don't be tempted to pile on too much shredded pork or it will be difficult to bite into the taco.
Top the tacos with 1 cup chopped onion and 2 tablespoons chopped fresh cilantro, dividing evenly. Squeeze over 2 tablespoons lime juice. Fold in half and arrange on a serving platter.
Serve surrounded by one or several of the following: remaining sauce, sour cream, black beans, avocado slices, salsa or tomato, lime wedges and fresh cilantro.