Soak black beans, great northern beans and kidney beans in water for at least 6 hours or overnight. Drain and boil in fresh water for 10 minutes. Drain and add to a 5- to 6-quart slow cooker.
Add oil, onion, celery, carrot, water, broth, barley, chili powder, cumin, oregano and salt to the slow cooker. Cover and cook until the beans are tender, about 3 hours on High or 6 hours on Low.