Sent a total of 4 boxes + a big suitcase for around 7,600 yen via Yu-Packゆうパック, a postal service by Japan Post. It's cheaper than using a moving company and renting a truck/van which can cost around 20,000 ~ 30,000 yen or more depending on the distance. The cost of using Yu-Pack depends on the distance and size of the package (Length + Breadth + Height).
The cost shown here is from Kinki Region to the rest of Japan
The dorm sells cardboard boxes at 320 yen for the large size (140cm) and at 220 yen for the small size (around 110cm *since it's over 100cm, it's charged at the 120cm size price). The large size boxes sold out during this week, so yup, do buy them early. Or, you can get free cardboard boxes from the Supermarket but they're are mostly within 100cm... Or, you can use a giant plastic bag to hold a small box, and add on to it! Then at the end, you wrap it up with other plastic bags (or a rice sack which I'd say is thicker) The downside is the end package isn't very sturdy, so pack only non-fragile stuff there (shoes, books, clothes, etc.).
NOTE: Don't pack in aerosols, batteries, lighters, stuff that don't go into your luggage when you check in for flights! The Post Office won't accept parcels with those and it'll get sent back to your old address...
On a side note, two more days left in Osaka and 5 more till uni entrance administration starts .__.