Many "parodies" I've come across are not take-offs of the songs themselves, but are reflections on the people who sing them, especially those who murder the best session favourites.
I nearly dropped a clanger at a session on Saturday -- I was about to do "The murder of the County Down" when someone jumped in with a poor rendition of the original. Glad I kept my mouth shut, 'cos he's a mate! (see Bev and Jerry's tip, above)

Some become nothing to do with the original whatsoever and end up as a set of lyrics put to an existing tune, on a different subject.
Where would we be without humour?
Have a Purrrrfect Xmas,
Rob