Expired residence card

I just graduated University in Japan. I am here on student visa and I just got a job in Tokyo and am applying for change of status. However, when I went to immigration, I was told to change my address first. I lived in Kyushu so I had to get a certificate to transfer address, but it took a week for me to receive it, and now my residence card is expired by 2 days. I am at immigration now but I have no idea what to expect or what is going on. Help.

You have probably illegally overstayed. Nobody here can tell you what will happen. Wait and see.

there was an option that you changed the student status to the special status by which you can stay in Japan, for a while, for looking for a job. I am sure that the university informed you, but you didn't listen it carefully.

http://www.moj.go.jp/ONLINE/IMMIGRATION/ZAIRYU_HENKO/zairyu_henko10_21...

It sounds like you left the renewal/change way too late. When I did my recent renewal (applying five weeks in advance which is usual for me) my lawyers mentioned that there was an automatic two month extension once the application was filed.
If you are over by two days because of a one week delay (because it appears you didn't follow the correct procedure on address notifications as well) then that sounds like you have a few issues to sort out. Contact an immigration lawyer for some advice - might be a good thing to do rather than relying on an internet forum - some lawyers give a first consultation for free.

Since a few days have passed since you�fve posted the question, I hope things have worked out somehow – the immigration bureau officer would know that it is them who told you to go change your address first, with which you complied, so I hope they will consider that delay with a kind eye, though I must say you were a bit late to start the whole process.

If they accepted your application for the change of resident status (for a delayed application, they might stamp �gaccepted as an exception�h or something like that into your passport) , that should go fine.
Best wishes.