Is it possible for users to login to Sakai via Google using OAuth2 as described here?
https://developers.google.com/accounts/docs/OAuth2Login
This would be similar to how users login to StackOverflow. If it's not currently possible, what would need to be built to allow this to happen?
Not currently. There is work to provide OAuth 1.0 authentication being tracked in Jira here: https://jira.sakaiproject.org/browse/SAK-22278
This includes a link to the code where you can try it out.
The code was originally designed to provide OAuth authentication for the RESTful webservices that are part of Sakai. The code also provides an Administrator tool where the OAuth application keys can be set, as well as a user tool that could be installed into each users My Workspace, where they can manage the tokens that have been set for the various applications.
OAuth 2 is slightly different and a bit more simplified, there is a good Stack Overflow discussion here: How is OAuth 2 different from OAuth 1?