Cannot connect to Facebook, hosts file seemingly ignored
Go to the Applications menu in settings -- at least that what I think it's called on Gingerbread, on on ICS it's just Apps -- select the Facebook app and clear the cache as well as the data. Then go to the /Android folder on your SD card and delete anything starting with com.facebook.

Finally, reboot your phone. If your problem was related to the Facebook app it should now be fixed.