I live in Indiana, will be moving to Minnesota briefly, and have been offered a job in Illinois. The job is only located in Illinois and my work in Minnesota and Indiana is not for this job. The signing bonus would be paid in 2009 while I still live in Indiana, but I would not start work until 2010. Which state(s) would I need to pay state income tax in on the signing bonus?

Yes, you must report bonus on your tax return for both the federal and state.
If it is reported on W2, it is your income. If it is reported on 1099-misc, then you will complete schedule C (Form 1040).