Trim excess fat from the pork shoulder and cut into 2-inch chunks.
In a slow cooker, combine pork, orange juice, lime juice, minced garlic, cumin, oregano, salt, and pepper.
Cover and cook on low for 7-8 hours or high for 4-5 hours until the meat is fork-tender.
Remove the pork from the slow cooker and shred with two forks.
Spread shredded pork on a baking sheet and broil for 3-5 minutes until golden and crispy.
Warm the corn tortillas in a dry skillet over medium heat for 30 seconds per side.
Divide the pork evenly between the tortillas.
Top with finely diced red onion, chopped cilantro, and thinly sliced radishes.