In a large bowl, whisk together the orange juice, lime juice, garlic, salt, cumin, oregano, black pepper, and bay leaves. Add the pork chunks and toss until fully coated. Cover and refrigerate at least 4 hours or overnight.
Preheat the air fryer to 350°F for 3 to 5 minutes. Drain the pork in a colander, discard the bay leaves, and reserve ¼ cup of the marinade. Pat the pork dry.
Toss the pork with olive oil. Arrange in a single layer in the air fryer basket, working in batches if needed. Cook at 350°F for 25 minutes, shaking the basket every 8 to 10 minutes.
Increase the temperature to 400°F and cook 10 to 15 minutes more, until the edges are deeply browned and the pork pulls apart easily. Internal temperature should read 195°F to 205°F.
Rest 10 minutes, then shred with two forks. Bring the reserved marinade to a simmer in a small pan and drizzle over the meat.
Return the shredded pork to the basket in a thin layer and cook at 400°F for 3 to 5 minutes to crisp the torn edges. Serve in warm tortillas with onion, cilantro, and lime.