I'm building a backoffice aplication and want to leverage our companies Google for Work directory for authentication. Is there a way to retrieve the groups a user belongs to within the organization? Maybe to get them in the claims when authenticating via OpenId?
While your question is a little unclear (what are you using to build your application? what exactly do you mean by "the groups a user belongs to"?), you can fairly easily retrieve user information using the Directory API.
For actual authentication, you can use Google as an Oauth identity provider.