Place the pork shoulder chunks into the slow cooker. Add the sliced onion and minced garlic on top.
Sprinkle the cumin, chili powder, oregano, salt, and black pepper over the pork. Pour the orange juice and chicken broth into the pot.
Cover and cook on low for 8 hours until the pork shreds easily with a fork. Shred the meat directly in the slow cooker and stir it into the juices.
In a mixing bowl, combine the shredded cabbage and carrot. Add the lime juice, olive oil, and a pinch of salt. Toss until the vegetables are evenly coated.
Warm the corn tortillas. Fill each tortilla with a scoop of the shredded pork and top with a spoonful of the fresh slaw. Finish with chopped cilantro.