Place squash in 6- or 7-quart slow cooker, overlapping as needed to fit. Cook, covered, on low until tender, 5-7 hours.
Remove squash from slow cooker; drain any cooking liquid from slow cooker. Using a fork, separate squash into strands resembling spaghetti, discarding the skin. Return squash to slow cooker. Stir in tomatoes, olives, oregano, salt and pepper, and sprinkle cheese on top; cook on low until heated through, about 15 minutes. Top with basil to serve.
Note: may sprinkle dried basil over top instead of fresh basil