Preheat oven to 450° F. Heat oil in a medium skillet over medium-high heat.
Cut chicken into thin strips, then add to the hot oil. Season with salt, pepper, and oregano; cook 6-8 minutes or until chicken is no longer pink. Shred or cut into bite-size pieces.
Place 4 tortillas on a baking sheet (or two if necessary); top each with chicken, cheese, and then a second tortilla.
Bake for 10 minutes, flipping halfway through.
Meanwhile, dice tomato, bell pepper, and avocado; slice olives and shred lettuce (if necessary).
Cut quesadillas into triangles and serve with toppings as desired; serve grapes on the side.