Preheat oven to 350°.
Heat a large nonstick skillet coated with cooking spray over medium-high heat. Add pork; cook 1 1/2 minutes on each side or until done. Remove pork; shred with 2 forks.
Add oil to pan; heat over medium-high heat. Add onion; sauté 4 minutes or until tender. Add garlic; sauté 1 minute. Remove from heat; stir in shredded pork, oregano, salt, and pepper.
Spread 1/4 cup New Mexican Red Chile Sauce over bottom of an 11 x 7-inch baking dish coated with cooking spray. Arrange 2 tortillas over sauce; top evenly with half of pork mixture and 1/2 cup sauce. Repeat procedure, ending with tortillas. Spread remaining sauce over tortillas. Sprinkle with cheese.
Bake at 350° for 20 minutes or until thoroughly heated. Cut each tortilla stack in half.