To prepare the kombu, rinse each strip of kombu briefly with running water. Cover with 2 cups of water and let soak for 15 minutes. Once the kombu is soft and pliable, tie a knot in each strip. Reserve the soaking liquid; this is the kombu dashi (soup base).
Drain the pack of konnyaku. Using a fork, pierce the konnyaku several times on each side. This will help the flavor to penetrate. Cut into four triangles. In a pot of water, boil for 2 minutes to remove the slightly fishy smell. Remove from the pot and set aside.
Slice daikon into 3/4-inch-wide rounds. Peel the skin, and make shallow cuts in the shape of a cross on each side of the daikon rounds.
Add knotted kombu, konnyaku, and daikon to a pot over medium heat with the 2 cups of reserved kombu dashi, 3 cups of water, soy sauce, mirin, and sake. Simmer for 25 to 30 minutes.
Remove the fish cakes from the oden set and rinse with boiling water to remove the oily film. Set aside the packet of broth from the oden kit; we will not be using it.
Add fish cakes and boiled eggs to the pot with the other ingredients and simmer for 30 minutes on medium-low heat. Do not allow it to boil, which can cause the broth to become cloudy.
Once finished, scoop your oden into bowls and serve with karashi for dipping.