Preheat oven to 350˚F. In a medium bowl, combine lime and orange juice, salt, and pinch cayenne pepper. Submerge skirt steak and marinate for at least 15 minutes.

Meanwhile, stir together ingredients for pico de gallo.

Heat oil in heavy large skillet over high heat. Add onion and bell pepper and cook until slightly tender. Push the vegetables to the sides of the pan and add the steak. Cook until desired doneness, about 3 minutes per side for rare. Transfer steak to cutting board. Let rest 5 minutes; slice.

Brush 4 tortillas with oil; place tortillas, oil side down, on 2 baking sheets. Spread half the tortilla with 1/4 each of the cheddar, steak, vegetables, and Jack cheese. Fold tortilla in half and brush top of quesadillas with oil.

Bake quesadillas for 5 minutes. Flip, and bake until heated through, 5 to 7 minutes more. Transfer quesadillas to plates. Cut into wedges. Serve with pico de gallo.