Facebook doesn't work due to "Failed to connect to 2a03:2880:10:1f03:face:b00c:0:26: Network is unreachable". Please see the below regarding this error.
stackoverflow.com/questions/11004624/failed-to-connect-to-2a032880101f03faceb00c026-network-is-unreachable-fr
Twitter worked fine with "You have successfully logged in".
LinkedIn failed with "42 - Failed to update contact: COM_CONTACT_WARNING_SAME_NAME". This is because you've Joomlas "User - Contact Creator" plugin enabled. I've now disabled it and LinkedIn now works fine with "You have successfully logged in".
Google failed with "Failed to connect to 2001:4860:8005::5f: Network is unreachable", which is similar to the issue with Facebook.
The Google and Facebook issues you'll need to take up with your host. Not a bug in plugin or its usage and nothing we can fix for you.