Preheat the oven to 350°F and lightly grease a 9×13-inch baking dish with nonstick spray. Set it aside. In a large skillet over medium heat, cook the ground beef until fully browned and no pink remains, then drain the excess fat. Incorporate the diced tomatoes, Rotel tomatoes with green chilies, salt, black pepper, onion powder, garlic powder, and tomato paste into the skillet, blending well. Reduce the heat and let the mixture simmer for 20 minutes to develop the flavors. Meanwhile, cook the egg noodles according to the package instructions, then drain thoroughly. In a separate bowl, combine the hot noodles with the sour cream, stirring until evenly coated. Spread this noodle mixture evenly across the base of the prepared baking dish. Pour the beef and tomato sauce mixture over the noodles, smoothing it out into an even layer. Sprinkle the top with cheddar cheese, Parmesan cheese, and mozzarella cheese in succession. Cover the dish with aluminum foil and bake for 35 minutes. Remove the cover and continue baking for an additional 5 minutes, until the cheese is bubbly and lightly golden.