In 3 1/2- to 4-quart slow cooker, mix all ingredients except mushrooms, spaghetti and oil.
Cover; cook on Low heat setting 8 to 10 hours.
Using 2 forks, break pork into bite-size pieces in cooker. Stir in mushrooms. Increase heat setting to High. Cover; cook 15 to 20 minutes. Meanwhile, cook and drain spaghetti as directed on package.
Stir oil into sauce. Serve over hot spaghetti. Sprinkle with cheese.