This is not a word that gets said frequently. If I heard it (or read it), I would assume that the speaker is very well educated and is very, very angry, and is in a situation that requires a certain amount of formality.

It's a rather old phrase. :) "Sheer" means "total" "Calumny" means lying about someone to damage their reputation A similar phrase is "calumny and slander"

Sheer = total, utter Calumny = slander, malicious lies intended to make the person being spoken about look bad Sheer calumny means that whatever bad thing being said about a person is being said with bad intent but is totally false