Over medium-high heat, warm olive oil in a small skillet. Add onion and celery and cook, stirring, until softened, 3 to 5 minutes. Add garlic and sauté 1 minute longer. Transfer mixture to a small bowl and let cool.
Place turkey in a large bowl. Add onion mixture, egg and oats. Gently blend the ingredients using your hands. Once blended, scoop out portions of the turkey mixture to form 20 meatballs around 1 1/2 inches in diameter.
Pour a small amount of barbecue sauce over bottom of slow cooker. Add meatballs, top with remaining sauce. Pour in 1/2 cup water. Cover and cook on high until meatballs are cooked through, 3 1/2 to 4 hours.