Preheat oven to 350 degrees F (175 degrees C). Arrange mushrooms, open-side up, in a baking dish.
Heat olive oil in a small skillet over medium heat; cook and stir celery until tender, about 5 minutes. Add blue cheese dressing, ranch dressing, buffalo wing sauce, and cream cheese to celery; cook and stir until cream cheese is melted and buffalo sauce is smooth, about 5 minutes.
Mix chicken and buffalo sauce together in a bowl until chicken is coated; spoon into mushrooms. Sprinkle Cheddar cheese over buffalo sauce.
Bake in the preheated oven until cheese is melted and golden, about 20 minutes.