Oden, often called hotpot by foreigners, is essentially a broth with lots of different ingrediants tossed in.
Commonly included are daikon radishes, fish cakes, boiled eggs, konnyaku (yam cake), and more. These ingredients are simmered in kelp-based stock for hours. It is usually cooked in a big ceramic pot at home.
Relevance to Urusei Yatsura
Oden seems to be Cherry and Sakura's favorite dish, even though they eat just about anything. Cherry always complains that Mrs. Moroboshi's oden is very light in the beef department, but with beef prices as high as they are in Japan, it's understandable.
The kids from Tomobiki High also find an oden bowl from space which magically fills with any food they ask for.