Not sure what a Nook R is (unless you're talking about the registered trademark R?), but going by the software version it sounds like it's a Nook Color (released 2010) or a Nook Tablet (released 2011). The HD and HD+ models use version 2 software.
The Color and Tab are tougher in that they don't have the Google Play store for apps and run very old versions of Android (2.x). OverDrive version 2.6.6 is the last version to run on that version of Android (which should work fine), but there is also the problem that B&N shut down the Nook App Store in March of this year pretty much abandoning Nook Color and Nook Tablet owners (newer Nook tablet models have the Google Play store). As I recall B&N didn't allow sideloading on those devices (well they briefly did on the Tablet, but took it away in an update) so installing OD 2.6.6 without an app store could be problematic.
The first thing that comes to mind would be wiping out the stock operating system and installing another version of Android (such as
Cyanogenmod) or using a
N2A Card type of solution. This would get you a newer version of Android that works with more apps.
Might be easier to grab the
new $50 Nook as it has more modern Android and the Google Play App Store. Screen resolution isn't great by modern standards, but if the Color/Tablet screen is okay for you the new one should be fine as it's the same resolution.