Broth: I used a piece of kelp (2x8 inches) which was first soaked in water for 30-40 minutes or longer (4 cups or about 1 liter) or whatever amount is appropriate for your vessel. I then put the pot on a medium low flame. When it comes to a boil, I reduce the flame to very low and add dried bonito flakes or "Kezuri (katsuo)bushi" 削り(鰹)節. I use a special large teabag-like bag called "Dashi bukuro" だし袋 in which the bonito flakes are placed and the opening sealed (about 20 grams). This is just for convenience so that I do not have to filter the broth later (I usually take out the bag with bonito flakes when the vegetables are all cooked). You could just put the bonito flakes in the pot and simmer for 10-20 minutes and then strain using a fine mesh strainer. You could also set aside a portion of unseasoned broth just in case the broth get too salty.
Daikon 大根: Daikon is a must in any oden and requires some preparation. I peel the skin and cut the peeled diakon into 1 to 1.5 inch thick rounds and bevel the sharp edges, mentori 面取り. I pre-cook the daikon in a separate pot with enough water to cover the daikon and one pinch of raw rice grains for 20-30 minutes and then transfer to the oden pot.
Carrot and potato: These items may not be most common items in oden but "Katsu-ya" served them and we like them very much. Just peel and cut into the size you like (not too small) and bevel the sharp edges and place it in the oden pot.
Boiled eggs: This is also the must-have item. I just boil eggs for 10 minutes, peel and place them in the oden pot.
Konnyaku コンニャク: It does not have much taste on its own and it is mostly for texture. most of Westerners will not appreciate this item but it is nonetheless a classic oden item. I make multiple shallow crosshatch cuts on both sides so that the broth will penetrate better. I then cut it into bite sized pieces (I cut this into a triangle which is traditional) then, par-boil it in plenty of water for one or two minutes. I drain the konnyaku and then place it in the oden pot.
Seasoning: At this point, I season the broth. I use soy sauce, mirin, sake and salt (I use salt to prevent the broth from becoming too dark which would happen if I added too much soy sauce to get the desired saltiness especially because I usually use a reduced salt soy sauce. Alternatively, you could use "light colored" soy sauce or "usukuchi shouyu" 薄口醤油. You may even like a dark broth, in that case, just use soy sauce. I cannot give you an exact amount but I will err on the side of under seasoning and go light on mirin (Vegetables add some pleasant natural sweetness). You can always adjust the seasoning later.
Chikuwa 竹輪: Cylinder-shaped fish cake (ground white fish meat with some binder and seasoning is boiled and lightly grilled and is sold frozen here in the U.S.) with a hole in the center shaped like a bamboo. Cut diagonally in the center (in the picture above it is shown in the center of the pot above the Daikon. In the picture below it is shown on the lower right).
Ganmodoki がんもどき: Deep fried oval patty made of tofu, egg white, black sesame seeds and other shredded vegetables (tan oval item with black specs -sesame seeds- in the picture below). Often, this is shortened as "ganmo".
Mochi in fried tofu pouch or mochi kinchaku 餅巾着: "Kinchaku" is a transitional Japanese purse. If you stuff anything in a tofu pouch or "Abura-age" 油揚げ, it is called "Kinchaku". Mochi 餅 is a rice cake made of pounded cooked rice. I cut one end of a small rectangular abura-age and place mochi inside and close the pouch with tooth picks (This pouch is shown between the eggs and kelp in the picture above). This is the same type of preparation I do for the new year soup. (If you are an oden officinado, you would order this item using its short form name "mochikin"). After 5-10 minutes, the mochi will become soft and sticky but contained in the tofu pouch it is easier to eat. (They are seen in the picture above between eggs and kelp.)
Just 10 minutes before serving, I add large cubes of tofu. Tofu should just be warmed through. As seen in the above picture, I garnish the tofu with chopped chives (or scallion). the daikon here is very soft and you can cut it with just chopsticks. The yellow stuff at the far right corner is Japanse mustard which is very hot but a necessary condiment for oden.
This is a perfect dish for cold winter days with sake. Warmed sake is the classic accompaniment but we like cold sake even with oden. Depending on what you like, you could use many other items in oden such as tough sinewy parts of beef, "Gyu-suji" 牛筋 cooked for long time, octopus leg "Tako" 鮹 (these are Kansai 関西 or West of Japan items), thick Japanese omelets with crab meat ("Kanitama" かに玉), many other types of fishcakes especailly white soft square ones called "Hanpen" はんぺん, and satsuma-age 薩摩揚げ. A bit unusual are "tara no shirako" タラの白子, which is the sperm sac of cod fish (It does not sound appetizing but it does taste very good), a Japanese style stuffed cabbage ロールキャベツ, a type of small conch or sea snail called "Tsubu" つぶ and so on. We really like oden but only problem for us is that there are so many goodies in one pot and it fill us up too quickly.