In English, we would describe oden as a soup. Some people would call it a stew, because the ingredients are in large pieces, but the dish is not cooked for many hours like a stew. You can describe it by listing the ingredients, like fish cakes and daikon. Tourists visiting Japan probably understand miso or miso soup, but not dashi and they will not know the difference.
So I would say uden is a kind of soup eaten in cold weather. It is like miso soup, but with large pieces of fish cake and fresh vegetables. There are no noodles, or udon, in uden.