Preheat oven to 350 degrees F. In a large skillet heat oil over medium heat. Add carrots, onion, and celery; cook for 8 to 10 minutes or until tender, stirring occasionally. Add green beans. Cook for 2 minutes more, stirring occasionally. Stir in tomatoes, barbecue sauce, balsamic vinegar, and oregano. Stir in beans and meatballs. Transfer mixture to a 2-quart casserole.
Bake, covered, for 10 minutes. Uncover. Bake for 20 to 25 minutes more or until heated through. Sprinkle with green onion tops just before serving.