Preheat the oven to 350 degrees F (175 degrees C). Lightly grease a 9x13-inch baking pan.
Heat oil in a skillet over medium heat. Add onion and celery and saute for 10 minutes. Remove from the pan. Add sausage; cook and stir, breaking it up with a spoon, until browned and crumbly, 5 to 7 minutes. Return onion and celery and cook for a few more minutes.
Transfer sausage mixture to a bowl and add stuffing mix and cranberries; gently stir until liquid is gone and ingredients are well coated. Place in the prepared baking dish and cover.
Bake in the preheated oven for 30 minutes. Remove cover and bake for an additional 5 to 7 minutes.