Heat a small non-stick skillet over medium-high heat with EVOO. Add garlic, salt, oregano, orange juice, lime juice and onion, and whisk until heated through.
Pierce pork roast as many times as you can with a sharp knife or fork. Pour marinade mixture (reserving a little for roasting) over pork, cover and let sit in refrigerator for 2-3 hours.
Using a suitable roasting pan or rack, sprinkle remaining marinade over pork and cook uncovered at 325°F. Roast until completely cooked (140-145°F internal temperature), about 40 minutes, basting occasionally.
Bring pan juices to a boil and simmer until the juice is reduced by half. Sprinkle some juice onto the pork when you put it in the Cuban sandwiches.