Generally speaking, the only way to separate the audio data from the video data is to demux it (look it up). Often, that's not very effective because the necessary audio header is part of the video header data. Thus, although you've split the audio from the video, most applications won't know how to handle the resulting audio file, because it lacks a header which indicates how to handle the data contained therein.
On top of that, but you'll still have all of the audio stuff that the video had, including sound effects, speech, dialogue, etc. And no, there's no way to remove that extra stuff from the audio of a video. Though, I don't know if that's the case with a 5.1 surround sound thing as you mentioned. Perhaps it'd work with that. I wouldn't know.
As for Youtube videos, you'll be best off with transcoding the FLV (or MP4 I suppose) file into a different audio format. Although it might be possible to separate the audio from the video (as I mentioned in my first paragraph), it won't be very useful. You'd be better of simply taking the video, and feeding it through some program that will intake a video, and output a WAV/MP3/OGG/whatever (oddly enough, I *just* barely used WinFF to do that with an FLV (MP4 actually) file).
So, about the only way to remove the sound effects/etc., is to recreate the audio data in question on some software/hardware device (that is, you'd have to replay the music yourself). There are other options, but they're all lossy to some degree, and they remove more audio stuff than just the sound effects/voices/etc.
I searched for [http://www.google.com/search?q=vocal+removal&ie=utf-8&oe=utf-8&aq=t&rls=org.mozilla:en-US:official&client=firefox-a]vocal removal[/url], as that might be something you're looking for. But I wouldn't suggest that as the best method. Specifically, check here. That looks like a fairly credible and useful page to look into, if you're seriously interested in cleaning up the audio on those videos as much as you can.
No doubt there's already a soundtrack of some sort of that, like with almost everything... looking for that is a hell of a lot easier, and it's guaranteed free of sfx. :P
If an OST exists, then I whole-heartedly agree that you should look that up. It'd be better audio quality than Youtube videos, it wouldn't have sound effects, and you wouldn't have to attempt to separate it out from the video. I didn't bother looking for an OST. If there's one out there though, then go for that. Any other means would be rather "un-smart."
If on the other hand no OST exists, then about the only thing you can do is what I said in my previous post. You'd still be better ripping it from a DVD than from Youtube though. Youtube videos aren't exactly the "cream of the crop" when trying to get good audio or video. Mouser X over and out.