In a medium skillet, heat oil over medium-high heat. Sauté peppers and onions until tender and slightly brown, about 3-4 minutes. Reserve.
Place tortillas on work surface. Sprinkle a quarter of the cheeses evenly over one half of each tortilla. Top with pepper-and-onion mixture and fold the tortillas into half-moons to cover the fillings.
Heat a large skillet over medium-high heat. Place one quesadilla in the skillet and cook on one side until brown, about 2 minutes. Flip and cook another minute, until brown and melted. Repeat with remaining quesadillas.
Cut into wedges and serve with salsa and guacamole on the side, for dipping.