Remove the skin and bones from the chicken, discard, and shred the chicken meat. Set aside.
In a Dutch oven or large stock pot, heat 2 tablespoons oil over medium-high heat. Add the onion and cook, stirring occasionally, until translucent, about 5 minutes. Add the garlic and cook, stirring, for 30 seconds. Add the chicken broth, enchilada sauce, and diced tomatoes with chilies. Raise the heat to high, bring to a boil, reduce heat, cover the pot, and simmer for 15 minutes.
While the soup is simmering, make the tortilla strips. Cut the tortillas into thin strips. Heat 2 tablespoons oil in a large skillet over medium-high heat. When the oil is hot, add one layer of tortilla strips at a time and cook until golden brown, about 15 seconds per side. Remove to a paper towel lined plate, sprinkle with a pinch of salt and repeat until all the strips are fried.
After the soup has simmered for 15 minutes, add the chicken, beans, and corn. Cook, covered, for another 5 minutes or until fully heated through. Serve the soup topped with the tortilla strips and any additional toppings you like.