In a large stockpot, heat oil to medium-high. Add carrots, celery, rutabaga, and onion. Sauté for 4-5 minutes, until vegetables begin to soften.
Turn heat to high and add broth, water, and all other ingredients, except turkey. Bring to a boil, then reduce heat and simmer for 40-50 minutes, until barley is soft. Add turkey and cook until soup returns to a boil.
Remove bay leaves before serving.