To a small frying pan over high heat, add 1 inches of vegetable oil and heat to 375 degrees F. Fry tortillas, one at a time, until golden and crispy. Drain on paper towels.
Heat olive oil in a large frying pan over high heat. Add sliced onion and 1/4 teaspoons salt. Cook, stirring, until onions are soft, about 4 minutes. Add oregano and cook until fragrant, about 1 minute. Add chicken and broth. Bring to a boil, lower heat to a steady simmer, and cook, partially covered, for 10 minutes to let flavors blend.
Meanwhile, in a small bowl, combine chiles, lime juice, orange juice, and remaining 1/4 teaspoons salt. Set aside.
To assemble: Divide turkey-onion mixture among the 8 tortillas, then top each with avocado, cabbage. Serve with serrano-citrus sauce.