Heat olive oil in a large skillet over medium heat. Add ground turkey and cook until no longer pink, about 5 minutes. Season with garlic powder, onion powder, salt, and black pepper. Stir in salsa and black beans; cook until heated through, about 5 minutes.
Cover tortillas with moist paper towels; microwave on high for 30 seconds.
Spoon turkey mixture into each tortilla. Sprinkle with Cheddar cheese.