Bring a large pot of lightly salted water to a boil. Cook egg noodles in boiling water, occasionally stirring until cooked through but firm to the bite, about 5 minutes. Drain.

Preheat the oven to 425 degrees F (220 degrees C).

Combine green beans, squash, peas, and carrots in a microwave-safe glass or ceramic bowl; cook until tender, 3 to 10 minutes. Rinse vegetables with cold water and drain.

Heat olive oil in a skillet over medium-high heat; sauté mushrooms in hot oil until tender, 5 to 7 minutes.

Whisk mushroom soup and milk together in a large bowl; add vegetables, mushrooms, tuna, onion, and Cheddar cheese. Mix in Worcestershire sauce, salt, and black pepper. Pour mixture into a casserole dish and top with French fried onions.