Preheat oven to 400ºF.
Place tortilla strips on a baking sheet, coat with cooking spray, and sprinkle with chili powder and pinch of salt. Bake until crisp, about 6 to 8 minutes.
Meanwhile, heat oil in a medium saucepan over medium heat. Sauté chicken thigh pieces until lightly browned, 1 to 2 minutes. Add bell pepper, jalapeño pepper, onion, and garlic, and cook until onions are tender, 2 to 3 minutes. Stir in tomatoes and cook 1 minute.
Add broth, water, cumin, oregano, and remaining 1/4 teaspoon salt to pan and bring to a boil over high heat. Divide soup among bowls and top with tortilla strips, cheese, and cilantro. Serve with lime wedges for squeezing.
Tip: The chile-flavored baked corn tortilla strips make this soup especially good. But in a pinch, you could substitute store-bought tortilla chips.