Hey. I have the 17-55 and 10-22. The 17-55 is sharper than the 10-22 in my experience. But it's not like the 10-22 is a slouch either, it's excellent.
And yes, the 10-22 hood will physically fit on the 17-55.... but it is not optimized for it at all and will be quite ineffective on that lens.
I don't have the 24-105 but I probably wouldn't want to own both the 17-55 and 24-105. What I would do is sell the 24-105 and get a 70-200. Either the 70-200 2.8, where you'll gain an extra stop, or the 70-200 F4 IS which is coming soon! It is only about $100 more expensive than the 24-105 according to B&H. And with ANY 70-200 model you can expect razor sharp images from. I dunno, just seems better to extend your range rather than duplicate a lot of it.