Sorry, I was mistaken. Calibre doesn't work because of the DRM. I am however able to read overdrive epubs delivered in .acsm file format on Linux.

First install Adobe Digital Editions in Wine.

http://kb2.adobe.com/cps/403/kb403051/attachments/setup.exe

When you try to open your downloaded .acsm you may have to go to All Programs and choose Wine Windows Program Loader. After a while your program picker will remember and offer Adobe Digital Editions when you try to open the .acsm.

You will get an error but it will display the url of the ebook. Enter that url into your browser and choose Open with Adobe Digital Editions. Worked for me.