In a large skillet, heat olive oil over medium-high heat. Add diced onion and ground turkey. Cook, breaking up the turkey with a spoon, until the turkey is browned, about 5 minutes.
Mix in minced garlic, tomato sauce, water, chili powder, cumin, paprika, oregano, salt, and black pepper. Reduce heat to low and let the mixture simmer for 10 minutes, stirring occasionally, until it thickens. Stir in the green chilis.
Warm the tortillas and spoon the turkey mixture onto each tortilla. Add shredded cheese and any other desired toppings. Serve immediately.