Heat the oil in a large pan over medium-high heat and brown the roast on all sides. Transfer the roast to a 4- to 6-quart slow cooker.
To the oil remaining in the pan, add the onions, celery, carrots, and garlic. Cook, stirring frequently, until tender, about 10 minutes. Add the tomato paste and stir to coat the vegetables; transfer to the cooker.
Pour the wine into the pan and deglaze, scraping up any browned bits, then pour the contents of the pan into the cooker. Add the mushrooms, salt, oregano, and tomatoes (as well as about 1 cup of their liquid). Cook 8 hours on low heat, or 4 hours on high heat.