Messenger server problems
Over the past 24-hours or so, it appears the Messenger servers have become desynchronized (or otherwise broken) and among other problems, are not reporting status information correctly. So you’ll see contacts with a display name of just their e-mail address, contacts online when they’re not, contacts offline when they’re not, and problems messaging between these contacts.
Normally these problems get resolved pretty quickly and signing out/sign in fixes the problem. Unfortunately In this case, it hasn’t proven to be very effective and these issues have been persisting.
Hopefully it will be resolved soon.
UPDATE: Everything seems back to normal now.