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:
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.
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.
There's no Darth Vidious?
Or, invidious, with a v, means "eVil"; insidious, with an s means "Sneaky". Does that help?