Arrange the spaghetti squash halves in the bottom of a slow cooker.
In a medium bowl, combine the tomatoes, olives, oregano, and 1/2 teaspoon each of salt and black pepper. Spoon the mixture over the spaghetti squash. Pour the olive brine in the slow cooker. Cover and cook on LOW for 6 to 8 hours or on HIGH for 3 to 4 hours.
When ready to serve, using a fork, "loosen" the squash slightly, creating spaghetti-like strands. Spoon the tomato sauce over the squash, top each piece with some tuna, string cheese, and basil and serve.