Preheat your oven to 350°F.
In a large Dutch oven or heavy-bottomed pot, heat the vegetable oil over medium-high heat.
Now by adding pork brown all sides for 5 minutes.
Once the pork is browned, remove it from the pot and set it aside.
Cook for 5 minutes by adding the onion and garlic to the pot until the onion is soft.
Add the cumin, oregano, chili powder, salt, and black pepper to the pot and cook for 1 minute, stirring constantly.
Add the pork back to the pot and pour in the orange juice, lime juice, and water.
Bring the mixture to a simmer and cover the pot with a lid.
Transfer the pot to the oven and cook for 2-3 hours, until the pork is tender and falls apart easily.
Once the pork is done, remove it from the pot with a slotted spoon and shred it with a fork.
Skim any excess fat from the surface of the cooking liquid and discard.
Return the shredded pork to the pot and mix well with the cooking liquid.
Serve hot with corn tortillas, salsa, guacamole, and lime wedges.