The Overdrive lending library PDFs are only readable using Adobe Digital Editions. The only EInk devices that include this are the Sony PRS-505 and PRS-700.
The Overdrive lending library MOBIs are readable by any device that supports (DRMed) MOBI. This includes the Kindle, but first you have to run the kindleFIX script, see
Visual Kindle Guide.
Unfortunately, as you have noticed, there are typically many more PDFs than MOBIs in most lending libraries.