Place the pork shoulder, orange juice, lime juice, garlic, cumin, oregano, salt, and pepper into a slow cooker.
Cover and cook on low for 8 hours until the meat is tender and shreds easily with a fork.
Transfer the pork to a cutting board and shred it into bite-sized pieces using two forks, discarding any large pieces of fat.
Heat a large non-stick skillet over medium-high heat and add the shredded pork along with a small amount of the leftover cooking liquid.
Sauté the meat for 5 minutes without stirring frequently to allow the edges of the pork to become crispy and caramelized.
Warm the corn tortillas in a separate dry pan until they are soft and slightly charred.
Assemble the tacos by filling the warm tortillas with the crispy pork and topping with red onion, cilantro, and radish slices.