Place the sliced onion and minced garlic in the bottom of the slow cooker.
Rub the pork shoulder all over with cumin, oregano, chili powder, salt, and black pepper. Set the pork on top of the onion and garlic.
Pour the orange juice and chicken broth around the pork.
Cover and cook on low for 8 hours until the pork is very tender and pulls apart easily with a fork.
Remove the pork to a cutting board and shred it with two forks. Return the shredded meat to the slow 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 chopped cilantro, diced white onion, and a squeeze of lime.