Hi, Daniel.
In a nutshell, Oauth is a way to delegate rights to access some personal/restricted data/functionality to some 3rd party (usually known beforehand) service on the Internet. And OpenID is extension to Oauth that just creates an additional special type of that data, a new scope called "openid" (and possibly a lot of other scopes designed to be associated with different kinds of identity attributes, too) and a new token called "id_token". So both were not quite designed to provide a totally independent autn/authz framework able to serve requests from a wide variety of users.
In your case, you could use OpenID for authentication, sending new user to Gluu and using a wide variety of authentication options it can handle, and then, after they've returned back to your web server hosting these APIs you want to protect with acquired id_token, process the token (+mb request more info about a user) and employ some kind of authorization you will implement by yourself.
Or you could go for UMA and completely "outsource" both authn and authz functionality to Gluu.
Whichever way you'll choose is up to you.