This is one of my big problems too actually, I have to play with my little cheapo headset mic all over the place. I tend to find it works best when like, I keep moving it around (carefully) when I go up and down in volume of even pitch (some times those things just catch and amplify the most ANNOYING sounds and you're like...NAUUGH.)
There's nothing you can do really easily with any software to get the ow-y-like parts out. I guess the only really really easy/not insane thing to do with it is to like, buy all this profession stuf with fuzzies and nice-ness all over it, but that's tinkering on crazy (and 'spensive). May as well just hire a back up band then XD.
So yeah, keep fiddeling with mics. It's easier with non-headset ones. You just have to be careful. I end up doing sectional re-recordings of mine around 50297298375 times before I'll let other people listen to it because I'm a nitpicker.
tThe poor people next door must think we have some sorta squeaky broken record problem.