Fred,
To really clear out the LinkedIn accounts, you'll want to delete the User Map connection. You don't need to delete the user though in Joomla though, though you can. Then, to tell LinkedIn that you are un-approving the application, you can login to linkedin.com and go to Settings -> Groups, Companies and Applications -> View your Applications. In there you can remove any applications that you've allowed to access your data, like your website. That will force you to approve it again the next time you login.
I'm assuming you're using JomSocial's Facebook functionality, not JFBConnects. I don't know the specifics of unlinking accounts there. However, in Facebook, you can go to Settings -> Apps and remove the website application as well. As for the redirect to the Facebook profile, again, I can't really help debug JomSocial's Facebook implementation, because I don't know how they've coded things.
That should make it so you're sure what account is logging in and verify that what should happen is happening.
Hope that helps!
Alex
How to delete the redirect to a profile and how to update a profile
