Preheat the oven to 325 degrees F. If using a Slow Cooker, turn it to high. I like to preheat my Slow Cooker, so the meat goes into a nice, hot cooker.
Mix the oregano, chili powder, cumin, salt and pepper together in a small bowl.
With your hands rub the pork chunks with the spice mixture (my kids usually volunteer for this, so ask your kids for help!) and put pork into a large Dutch oven, or Slow Cooker. Add the onion, garlic, chicken stock, tomato puree, and honey. Cut the orange and lime in half, squeeze the juice into the pork mixture, and add the halves to the pot, too. Stir everything together, and put the Dutch oven on medium heat. Once the mixture starts to simmer, transfer to the oven and cook, covered, until the pork is tender and easily shreds, about 2 ½ hours. If using a Slow Cooker, cook on medium high for about 8-10 hours. You know it’s done, when you can easily shred the pork.
Remove the meat from the Dutch oven to a cutting board. Cover with foil to keep it warm. Set the Dutch oven over medium heat and reduce the liquid until it thickens up and becomes slightly syrupy, about 10 – 15 minutes. If you can’t put your Slow Cooker insert on the stove, transfer the sauce to a medium pot and reduce the sauce. When the sauce is syrupy, reduce heat to low so the sauce stays warm. Shred the meat and add back to the sauce. Stir so the sauce coats the meat.
Serve with tortillas, cilantro, sour cream, cabbage and any other of your favorite toppings. I love to add some sliced avocado and my kids usually douse theirs with salsa.