Looking for the right way: Spring Social + Spring RESTful API + Spring WebApp + Mobile Clients
The solution we use it to secure our rest-webservices using spring security, with a cookie based remember me service. This uses well documented traditional spring-security techniques.
We then plugged in spring-social to our system, which then simply logs in the user as normal using spring secruity. The social api looks up the, for example, facebook id in your db table, if it finds existing connection logs the user in using their account on your system (and can redirect to sign up page etc).
I suggest breaking down the question into more specific areas.