Nabe refers to a pot of hot vegetables and meat or fish in a broth. Oden is a form of that and is very popular, especially in winter. It is served both in restaurants and from street vendors with their carts.
Although there are many varieties, the original oden consisted of tofu dabbed with miso, skewered and grilled over coals. The idea of the vendor's carts began to catch on in Edo when it was given the name odengaku. It eventually became shorted to oden and referred to chunks of konnyaku (which is a dense jelly made from a starchy root) and taro along with tofu. These were eaten from a stick although now the skewers have been replaced by the use of chopsticks.
The material in the vat that this is all cooked in can consist of giant radishes, tofu, fish paste, dried kelp, fish dumplings, octopus, squid, mushrooms and other items. The stock that this all cooks in is also quite important, picking up flavors form the various items that are being cooked. This is another of the foods that is also relatively low in price, adding to its popularity.