In a Dutch oven, combine the spices (oregano, chili powder, cumin), pork, onion chicken broth/stock, tomato paste, honey, orange and lime juice. Give it a good stir. Over medium heat, bring mixture to a simmer.
Transfer to the oven and cook, covered, until the pork is tender and easily shreds, about 1 hour and 45 minutes.
Remove the meat from the Dutch oven to a cutting board. Set the Dutch oven over medium heat and reduce the liquid until it becomes slightly syrupy, about 10 minutes.
Meanwhile, shred the meat and return to Dutch oven once liquid is reduced. Allow pork to soak up remaining liquid. Season with salt & pepper as desired. Serve with corn tortillas and garnish as desired.