Bring a large pot of lightly salted water to a boil. Cook egg noodles in the boiling water, stirring occasionally, until cooked through but firm to the bite, about 5 minutes; drain.
Heat a large skillet over medium-high heat. Cook and stir beef in the hot skillet until browned and crumbly, 5 to 7 minutes; drain and discard grease. Season beef with Greek seasoning, salt, and pepper.
Heat vegetable oil in a separate skillet over medium heat. Cook and stir mushrooms in hot oil until tender, about 5 minutes; add to ground beef.
Stir sour cream into ground beef mixture; cook and stir until hot, about 5 minutes. Serve over egg noodles.