1. In the bowl of a multicooker, toss together pork, chiles, oregano, cumin, cayenne, and 4 teaspoons salt. Add orange and lime juices, onion, garlic, and 1 cup water. Secure lid of multicooker. Choose "Meat/Stew" setting and set timer for 50 minutes. Once cycle is complete, allow pressure valve to release slowly. Carefully remove lid. Discard onions and garlic. In the bowl of the multicooker, use two forks to shred pork into bite-size pieces.

2. Using tongs, place a tortilla directly on a gas flame or in a heavy skillet over high heat. Cook, flipping once, until lightly toasted and charred in places, about 30 seconds. Wrap in a clean kitchen towel. Repeat with remaining tortillas. Serve carnitas in tortillas with cabbage, avocado, cilantro, cheese, and a squeeze of lime.