Disclaimer: I'm not a lawyer, but I've had to deal with copyright issues at my work. The sad, sick fact about U.S. copyright is that much of it is random. There are things that are clearly infringement, things that are clearly not, and then there's everything else. The everything else part can boil down to who has the better lawyer, what mood the judge is in, or whether or not the copyright holder deems it in his or her interest to make a stink.
Parody is accepted under fair use. If you're doing a genuine parody and distributing it in a place where you aren't making any money (like YouTube), you're almost certainly fine. Put the same thing up for sale, and you may get a letter in the mail. That doesn't mean you're not protected; it just means someone probably wants a piece of your action.
As for performing cover songs on YouTube, unless the songs are in public domain, you're in copyright violation. That's all there is to it. For 99.99% of all such cases, if the copyright holder wants to complain, they'll send a takedown notice to YouTube and that'll be the end of it. Takedown notices are part of the Digital Millennium Copyright Act. When YouTube or some other host receives a takedown notice, two things happen: the site takes down the allegedly offending content and they send the uploader a notice of having done so. The uploader is given an opportunity to respond and explain why he or she believes the takedown to be improper. If there's no response from the copyright holder in a certain amount of time, the content goes back up. If the copyright holder responds, the uploader is probably going to court.
There's a decent explanation of this
here...
In any event, I wouldn't sweat it too much. Technically speaking, almost every time a performer sits down in a coffeehouse and strums out a few tunes, they're violating copyright. Every time someone passes out photocopies of someone else's song at a uke jam, they're violating copyright. The sheer quantity of cover songs on YouTube shows that most artists and publishers don't consider this stuff to be much of a threat to their livelihoods, and they're right.
Illegal downloads on the other hand...
-Pete