Preheat oven to 450 degrees, with rack in lower third. In a large skillet, heat oil over medium-high. Add onion and garlic and cook, stirring occasionally, until onion begins to soften, 4 minutes. Add orange and lime juices and bring to a boil. Season with salt and pepper, stir in oregano, and remove from heat.
Pat pork dry with paper towels. Season generously with salt and pepper and place in a heavy-bottomed ovenproof pot (pork should fit snugly). Pour onion mixture on and around pork, leaving some on top. Roast, uncovered, 30 minutes. Remove pot from oven and reduce temperature to 350 degrees. Ladle onion and cooking juices over pork. Cook, uncovered, until cooked through (an instant-read thermometer inserted in thickest part of pork should read 155 degrees), 1 1/2 hours, basting pork with onion and juices every 30 minutes. Let rest 15 minutes before slicing. To serve, skim fat from cooking juices and spoon sauce over sliced pork.