- 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.