Preheat the oven to 350 degrees F. Lightly butter a 13x9x2-inch casserole dish.
In a bowl, combine the turkey, mushroom soup, chiles, salsa, olives, onions and cumin.
Scatter half of the tortilla strips over the bottom of the prepared casserole dish. Cover with half of the turkey mixture and then all of the Monterey Jack cheese. Repeat with the remaining tortilla strips, the remaining turkey mixture, and the Cheddar cheese.
Bake until bubbly, about 45 minutes. Serve hot or microwave to reheat.