Preheat the oven to 350°F (175°C).
In a large bowl, combine the shredded chicken and taco seasoning mix. Stir in the salsa and sour cream until well mixed.
Add the black beans, corn, and half of the chopped green onions to the chicken mixture. Stir to combine.
In a 9×13 inch baking dish, spread half of the tortilla strips evenly on the bottom.
Spread half of the chicken mixture over the tortilla strips.
Sprinkle half of the shredded cheddar cheese and half of the shredded Monterey Jack cheese over the chicken layer.
Repeat layers with the remaining tortilla strips, chicken mixture, and cheeses.
Cover the casserole with aluminum foil and refrigerate for up to 24 hours if making ahead.
When ready to bake, remove the casserole from the refrigerator and let it sit at room temperature for 15 minutes.
Bake uncovered for 30 to 35 minutes, or until the casserole is heated through and the cheese is melted and bubbly.
Remove from the oven and let stand for 5 minutes before serving.
Garnish with the remaining chopped green onions and fresh cilantro.