Preheat oven to 375 degrees F. Lightly grease a 3-quart rectangular baking dish; set aside. Cook noodles according to package directions; drain. Rinse with cold water; drain again.
Meanwhile, in a medium saucepan, heat butter over low heat. Add flour; cook and stir for 4 minutes (be careful not to let flour brown). Gradually whisk in milk, salt, and pepper. Cook and stir until slightly thickened and bubbly. Reduce heat; stir in Parmesan cheese, Swiss cheese, and sherry. Cook and stir until cheeses are melted.
In a medium bowl, combine Pecorino Romano, mozzarella, provolone, and cheddar cheeses.
To assemble, spread one-fourth of the sauce in prepared baking dish. Sprinkle with one-fourth of the cheese mixture. Layer with one-third of the noodles, one-fourth of the sauce, half of the tomatoes, half of the mushrooms, half of he salmon, and one-fourth of the cheese mixture. Repeat layering noodles, sauce, tomatoes, mushrooms, salmon, and cheese mixture. Top with the remaining noodles, remaining sauce, and remaining cheese mixture.
Bake, uncovered, for 50 to 55 minutes or until edges are bubbly and top is lightly browned. Let stand for 15 minutes before serving. Makes 12 servings.