In a large bowl, combine the pork shoulder chunks with olive oil, salt, black pepper, cumin, oregano, garlic powder, and onion powder. Mix until the pork is well coated.
Place the seasoned pork in the slow cooker. Add the orange juice, lime juice, quartered onion, and smashed garlic cloves.
Cover and cook on low for 8 hours or high for 4 hours, until the pork is tender and easily shredded with a fork.
Once cooked, remove the pork from the slow cooker and shred it using two forks. Return the shredded pork to the slow cooker and mix it with the juices.
To serve, heat the corn tortillas in a dry skillet over medium heat until warm and pliable. Fill each tortilla with the shredded carnitas and top with fresh cilantro. Serve with lime wedges on the side.