Remove skillet from heat and add in the condensed cream of chicken soup, condensed cream of mushroom soup, diced tomatoes with green chilies, chili powder, dried oregano, and shredded chicken. Mix until well combined.
Place half of the tortillas in an even layer in the bottom of a 9×13-inch baking dish. Top with half of the chicken mixture then half of the cheddar cheese. Repeat until not ingredients remain.