Trim excess fat from the pork shoulder and rub all sides with the dried oregano, cumin, garlic powder, onion powder, sea salt, and black pepper.
Place the seasoned pork in a slow cooker and pour the orange juice and lime juice over the top.
Cover and cook on low for 7 to 8 hours or on high for 4 to 5 hours until the meat is fork-tender and easily shreds.
Remove the pork from the slow cooker and shred it using two forks, discarding any remaining large pieces of fat.
Preheat your oven broiler to high and spread the shredded pork onto a large baking sheet.
Drizzle a small amount of the cooking liquid from the slow cooker over the meat and broil for 3 to 5 minutes until the edges are crispy and golden.
Warm the corn tortillas in a dry skillet over medium heat for 30 seconds per side until pliable.
Assemble the tacos by dividing the crispy pork between the tortillas and topping with diced red onion, chopped cilantro, and thinly sliced radishes.
Serve immediately with a fresh squeeze of lime from the wedges.