Cut roast into 2 pieces that will each fit easily inside the pot. Pat pork dry. Rub pork all over with salt and pepper.
Set your Instant Pot to sauté on Normal. When the display says Hot, add 1 tablespoon (15 mL) oil and heat until shimmering. Working with one piece at a time, add pork and cook, turning, for 8 minutes or until browned on all sides, adding more oil as needed between batches. Using tongs, transfer pork to a plate as it is browned.
Set aside ½ cup chopped onions for garnish. Add the remaining onions to the fat remaining in the pot and cook, stirring often, for 5 to 7 minute or until softened. Add the garlic and cook, stirring, for 1 minute or until fragrant. Press Cancel. Stir in chicken stock, orange zest, orange juice, oregano leaves, red pepper flakes, and bay leaves, scraping off any browned bits from the bottom of the pot. Return pork and any accumulated juices to the pot, turning to coat.
Close and lock the lid and turn the steam release handle to Sealing. Set your Instant Pot to pressure cook on High for 60 minutes.
When the cooking time is done, press Cancel and let stand, covered, until the float valve drops down. Remove the lid. The pork should be fork-tender. (If more cooking time is needed, continue pressure cooking on High for 5 minutes, then quickly release the pressure.)
Transfer pork to a large bowl or cutting board. Using two forks, shred pork. Discard any excess fat.
Meanwhile, discard all but ⅔ cup liquid from the pot. Discard bay leaves. Set your Instant Pot to sauté on High. Add shredded pork to the pot and cook, stirring often, until liquid has evaporated and pork is slightly crispy.
Garnish with cotija and cilantro. Serve with salsa and lime wedges, if using.