Place the pork chunks, sliced onion, and minced garlic into the slow cooker. Sprinkle the cumin, oregano, chili powder, and salt over the meat.
Pour the orange juice and lime juice into the slow cooker. Stir the ingredients gently so the spices coat the pork.
Cover and cook on low for 8 hours until the pork shreds easily with a fork.
While the pork cooks, combine the shredded cabbage, shredded carrot, chopped cilantro, olive oil, and remaining lime juice in a bowl. Add 1/2 teaspoon salt and toss until the slaw is evenly coated. Set the slaw aside in the refrigerator.
When the pork is done, remove it from the slow cooker and shred it with two forks. Return the shredded pork to the cooker and stir it into the juices.
Warm the corn tortillas in a dry skillet or microwave. Fill each tortilla with pulled pork and top with a spoonful of fresh slaw.