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.

Wikipedia described it as; "Oden is a Japanese winter dish consisting of several ingredients such as boiled eggs, daikon, konjac, and processed fishcakes stewed in a light, soy-flavoured dashi broth. Ingredients vary according to region and between each household." I think that is perfectly fine, give your own twist to it and you are good to go! :) Let me know if that helped you enough or whether you need some further assistance.