Preheat oven to 375°F (190°C).
In a large bowl, combine the cooked shredded chicken, salsa, black beans, corn, ground cumin, chili powder, garlic powder, onion powder, and salt. Mix well to evenly distribute the spices.
Lightly grease a 9×13-inch baking dish.
Spread a thin layer of the chicken mixture on the bottom of the baking dish.
Sprinkle a layer of tortilla strips over the chicken mixture.
Sprinkle 1/3 of the shredded cheddar cheese and 1/3 of the shredded Monterey Jack cheese over the tortillas.
Repeat layering two more times, ending with cheese on top.
Cover the casserole tightly with aluminum foil and refrigerate if making ahead, or proceed to bake immediately.
If refrigerated, remove from fridge and let stand at room temperature for 15 minutes before baking.
Bake the casserole covered for 25 minutes.
Remove the foil and bake for an additional 10 minutes, or until the cheese is melted and bubbly.
Remove from oven and let cool for 5 minutes.
Top with sour cream and chopped fresh cilantro before serving.