In a large plastic storage bag, mix the lime juice, Worcestershire sauce, 2 tablespoons of the oil, chili powder, oregano, and cumin. Add the pork strips and toss. Cover with plastic wrap and refrigerate, at least 1 hour and up to 8 hours.
Heat a large (12-inch) nonstick skillet over medium-high heat. Add 1 tbsp of the remaining oil and tilt the skillet to coat the bottom. Add the onion, red pepper, and green pepper. Stir-fry until the vegetables are crisp-tender, about 3 minutes. Add the garlic and cook for 1 minute. Transfer to a bowl and set aside.
Remove the pork from the marinade, pouring the marinade into a bowl. Stir the beef broth and tomato paste into the marinade and set aside.
Heat the remaining 1 tbsp oil in the skillet over medium-high heat. In 2 batches, cook the pork strips, adding more oil as needed, stirring often, until the pork is browned, about 4 minutes.
Return the pork and peppers to the skillet. Add the broth mixture and cook until the sauce is slightly reduced, about 3 minutes. Season with the salt and pepper.
Spoon the rice into individual serving bowls, top with the pork stir-fry, and sprinkle with the cilantro. Serve immediately. Pass bowls of avocado and sour cream on the side, if desired.