Has Grey's Anatomy stopped airing until Jan 14th?

Yup it sure has. But they are doing things called Webisodes every thursday on ABC.com at the same time as Grey's would usually be on.

Yes. Grey's Anatomy has stopped airing but ABC is showing the earlier episodes of this season until January 14th.

yes they have stopped airing new episodes till the 14th but they are showing reruns of season 1 right now on lifetime.