Can you ensure that you're using the latest JomSocial? There was an issue with all versions before 3.2.0.4 (I believe) where user's couldn't login properly. I know you said you're on the latest, but letting me know the exact version numbers helps. For more information on that issue, please see
this blog post
from JomSocial.
As for what's happening, I'm honestly not sure, but here's the first steps I'd recommend to try and narrow things down:
* Disable SEF URLs in the Joomla -> Global Configuration area or any 3rd party extensions you're using
* Disable caching in the Joomla -> Global Configuration area
I hope that helps get you started, but if not, let me know your version numbers and we'll see what we can do.
Thanks,
Alex