Preheat oven to 350°.
Heat 2 tablespoons olive or vegetable oil in a large skillet over medium heat. Cook 2 pounds chicken breasts until browned and cooked through. Remove from pan and shred into bite size pieces.
Melt 2 tablespoons butter in same skillet over medium heat. Add 1 small onion, diced, and sauté until tender. Add 1 medium green bell pepper, 1 medium red bell pepper and 1 garlic clove, and sauté 3 to 4 minutes more.
Stir in 1 cup chicken broth, cream of mushroom soup, cream of chicken soup, diced tomatoes and green chilies, 1/2 teaspoon salt, 1 teaspoon dried oregano, 1 teaspoon ground cumin, and 1 teaspoon chili powder. Return the shredded chicken to the pan. Cook, stirring occasionally, for about 5 minutes, until mixture is heated through.
Lightly grease a 9x13 inch baking dish. Spread about 1/4 cup of the chicken mixture in the bottom of the pan to coat.
Layer with half of the 8-10 8-inch flour tortillas, cut into 1/2-inch strips. Top with half of the chicken mixture and 1 cup of 2 cups grated Cheddar cheese. Repeat layers once (tortilla strips, chicken mixture, cheese).
Cover and bake at 350° for about 40 minutes. Uncover and bake for and additional 5-10 minutes. Let stand 10 minutes before serving.