iPod Classics didn't run iOS.
Dunno about how to save them through iTunes, but I'd bet if you used one of those hack tools to mount the HD in a read/writeable format they would be on the HD in an mp3 or m4a format. The problem, as I recall, is that Apple named files numerically or alphanumerically on the HD and used a database to present thsoe files with nice names. So if you could setup the Classic so those were the ONLY audio files on the drive you'd probably have an easier time finding them. Figuring out which is which, well, that could be tricky.
Thanks MonkeyBoy. I don't have the courage to start fiddling too far with this irreplaceable machine to be honest.
I've got 464 Podcasts, which I patiently went through, one at a time, selecting 'Save episode' only to have them all revert to unsaved the next time I connected the Classic to iTunes. That's the pedestrian level I operate at most of the time. Imagine my torment
They are BBC Radio Podcasts of a programme called 'In Our Time'. I have them all going back to January 2008. The Beeb has an archive of older IOT programmes going back to 1998, any or all of which can be downloaded. These archived episodes are classed as 'Genre - Podcast', 'Kind - MPEG audio file', and are immune to this 'saved/unsaved' nonsense.
As my old Nan used to say, "Life's just a bag of peas."