Go to https://www.icloud.com and sign in with your Apple ID and (new) password. Click the big green "Find my iPhone" icon. Then, click the Devices button at the upper left. Does your iPod appear in the list?
The fact that the thief was able to download music tells me the iPod did not have a passcode enabled. That's not good.
Its serial number is not useful other than to establish ownership and for purposes of filing a stolen property report. Other than lending a sympathetic ear, Apple won't be able to do anything.
If it's any consolation the thief won't be able to update apps or purchase anything else without your Apple ID password. For it to be useful to anyone, it will eventually have to be totally erased.
This is their official word on the subject:
Reporting a lost or stolen Apple product
If you have lost or found an Apple product, please contact your local law enforcement agency to report it. Although Apple does not have a process to track or flag lost or stolen product, you can use My Support Profile to find a list of serial numbers for items purchased or registered with your Apple ID.
Consider using this: http://www.stolenlostfound.org/
Though it contains no remarkably enlightening information, you might also find the following checklist useful:
http://www.ipadastic.com/tutorials/how-to-track-and-report-stolen-ipad
It applies in general to stolen iPods as well.
