There is a big problem in the following case:
User has Windows XP, ClearType turned off, Google Chrome and website is using Google Web Fonts.
Fonts look very “jerky” in this case and only in Chrome.
css “-webkit-font-smoothing” won’t do any good.
Also, I noticed that large fonts are not so terrible. You can see in the pic big fonts and they look okay.
Is there a solution for a user with these settings to have nice looking fonts?

With ClearType turned off there is really no hope. Even native system fonts look bad with ClearType off.
I believe IE8 and above automatically override the OS settings on XP and turn ClearType on, but I don’t think there’s a way for a non IE browser to do that.
If you care about the relatively small percentage of visitors who are in this category you’ll need to spend many hours choosing and testing a better font.
My advice is to not worry about it – Those users will be quite accustomed to seeing horrible fonts all over the web because of their ignorance of or inability to change system settings.