All ingredients ready? Let's begin!
In a glass baking dish or a resealable gallon baggie, place the chicken strips, 2 tablespoons of olive oil, lime juice, chili powder, cumin, oregano, salt, and pepper. Toss to coat well. Cover or seal and place the chicken in the refrigerator for 45 minutes.
Remove the chicken from the refrigerator and set it aside while you cook the peppers and onions.
In a large sauté pan over medium-high heat, warm 1 tablespoon of olive oil. Add the onions and peppers to the pan and cook until just wilted, approximately 5 minutes. Season with salt and pepper. Remove the peppers and onions to a platter or bowl.
Add the chicken to the pan and sauté until completely cooked through, stirring a few times, approximately 8 minutes. Transfer the chicken to a plate.
Reduce the heat to medium. Wipe the pan out with a paper towel. Add a small amount of the remaining olive oil to the pan.
Place a tortilla in the pan. Top it with 1/4 each of the onions and peppers, chicken, avocado, and cheese. Top with another tortilla. Cook until golden and the cheese has melted, approximately 3 minutes per side. Repeat until all the quesadillas are cooked. You can keep them in a warm oven until all are cooked and ready to serve.
Transfer the quesadillas to a clean cutting board and cut each into 4 wedges. Serve while warm with sour cream and salsa on the side.