Preheat oven to 180 degrees C. Line a baking tray with baking paper.
In a large frying pan, fry the chicken strips in vegetable oil until they are no longer pink. Add the onions and fry (stirring constantly) until they are translucent. Mix in the salsa (you may want to add more to taste).
Place the tortillas between two damp pieces of paper towel and microwave on high for 1 minute.
Fill half of 1 tortilla with the chicken mixture and cheese, then fold the tortilla over the full half. Repeat with remaining tortillas and filling. Arrange the quesadillas on the prepared baking tray.
Bake the quesadillas in the preheated oven until the cheese has melted. Cut the quesadillas into fours.