Preheat the oven to 400°F. Cut the spaghetti squash in half lengthwise and remove the seeds. Rub the oil into the squash halves. Bake on a baking sheet for 15-20 minutes, or until the squash is fork-tender.
Scoop out the cooked squash "noodles" and add them to the slow cooker insert. Toss with Parmesan cheese and Italian seasoning. Add the tomatoes and top with the shredded mozzarella. Cover and cook on low for 4-5 hours or on high for 2 hours. Serve when the cheese is hot and bubbly and the flavors have melded.