How do I delete photos in photo albums without using iTunes? I have bought a used iPod which the previous owner had loaded photo albums on. I do not have iTunes and it will not let me delete the photos/photo albums without it.

How do I delete the photo albums that are on this device?
One approach would be to wipe the iPod (Touch, I assume?). Obviously doing so will erase all of those photos, any music, you have on the device, as well as all of your apps.

You do this by going to Settings -> General -> Reset -> Erase All Content and Settings.

If it is a new enough device to have iCloud backup, you could always disable photos, before wiping the device, and then restore using the iCloud backup. However, if you have photos on the device that you want saved, this approach will not work.