In a large bowl. combine the juice of the 2 limes, garlic, cilantro, 2 tablespoons of the oil, vinegar, salt, cumin, oregano, pepper and chili powder. Whisk together until well-blended.
Add beef, cover and marinate in the refrigerator for about 30 minutes to 1 hour. Turn occasionally.
In a bowl, combine bell peppers, onions, 1 tablespoon of the oil and juice of the remaining 1 lime. Season with salt and pepper to taste. Gently toss to fully coat and set aside.
Drain meat from marinade and pat dry. Discard marinade. Season both sides with salt and pepper to taste. Cut beef across the grain into 1/4-inch thick slices.
In a wide pan over medium-high heat, heat remaining 2 tablespoons oil until hot. Add beef and cook for about 3 to 5 minutes. Remove from pan and keep warm.
In the same pan over medium-high heat, add bell peppers and onions and cook, stirring regularly, for about 1 to 2 minutes or until tender yet crisp. Remove from pan and keep warm.
In another pan, heat tortillas for about 30 seconds on each side or until warm and pliable.
To assemble fajitas, divide meat and vegetable mixture onto warmed tortillas. Serve with guacamole, pico de gallo and lime wedges.