Can anyone give me a really short & sharp distinction between these two words? Are they notorious for often getting mixed up?
Sorry, but Malvolio's answer is too simple in some parts, and the other parts are simply wrong. Let's see what NOAD has to say:
invidious |inˈvidēəs| adjective (of an action or situation) likely to arouse or incur resentment or anger in others : she'd put herself in an invidious position. • (of a comparison or distinction) unfairly discriminating; unjust : it seems invidious to make special mention of one aspect of his work.
That's not eVil. It's not even evil. It can be used as a pejorative, but it is decidedly not simply a synonym for bad.
insidious |inˈsidēəs| adjective proceeding in a gradual, subtle way, but with harmful effects : sexually transmitted diseases can be insidious and sometimes without symptoms. • treacherous; crafty : tangible proof of an insidious alliance.
This in a sense means "sneaky" — but that is far short of a definition. Insidious is actually more "evil" than invidious, as you can see.
If you need a mnemonic, use the "v" in invidious to represent the "v" in "visible": it's something you can see. If something is insidious, on the other hand, it's something harmful which derives its power from the fact that you don't notice it.