There's really two separate things that these systems can do.
The classic OAuth scenario is like this:
site A: Wikipedia user A site B: Huggle
Site B initiates a special login on site A using a shared secret; on success, site A passes back authentication tokens to site B which verify that user A allowed site B access.
Site B then uses those tokens when it accesses site A, in place of a username/password directly.
OpenID, SAML, etc seem to be more appropriate for this scenario:
site A: Wikipedia site B: University user B
These systems allow user B to verify their identity to site A; one possibility is to use this to associate a user A' with the remote user B, letting you use the remote ID verification in place of a local password authentication. (This is what our current OpenID extension does, basically.)
These are, IMO, totally separate use cases and I'm not sure they should be treated the same.
The Extension:OpenID can be used for both cases ( given, that you set $wgOpenIDClientOnly = false; ) https://www.mediawiki.org/wiki/Extension:OpenID .
"The extension makes a MediaWiki installation OpenID 2.0-aware and lets users log in using their OpenID identity - a special URL - instead of (or as an alternative to) standard username/password log in. In that way, the MediaWiki acts as Relying part (RP) = OpenID consumer.[1]
*As an option, it also allows the*_*MediaWiki to act as OpenID provider*, _so that users with an account on that wiki can use their userpage URL as OpenID with which they can log in to other OpenID-aware web sites."
set $wgOpenIDClientOnly = false; if you want this
Tom.