Cut the pork shoulder into larger chunks for easier cooking and marinating.
In a bowl, combine the orange juice, lime juice, minced garlic, cumin, oregano, salt, and pepper. Marinate the pork in this mixture for at least 30 minutes, or preferably overnight.
In a large Dutch oven or slow cooker, heat olive oil over medium-high heat. Sear the pork on all sides until golden brown.
Add the sliced onion and pour in the marinade. Reduce heat to low, cover, and cook for 3-4 hours, or until the pork is very tender.
Once the pork is tender, shred it with a fork. Then, crisp it up in a skillet over medium heat for a more satisfying texture.
Warm the tortilla wraps, then fill them with the cooked carnitas, fresh cilantro, and lime wedges.
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