WordPress MediaWiki integration
The tutorial WordPress, bbPress & MediaWiki should get you on the right track to integrating MediaWiki into your WordPress install. It's certainly going to be a lot easier than hacking WordPress to have wiki features, especially with the sort of granular permissions you're describing.
Both MediaWiki and Wordpress support OpenID:
http://www.wordpress.org/extend/plugins/openid/
http://www.mediawiki.org/wiki/Extension:OpenID
Though, I think for automatic logins (after you log in to one, you automatically log in to the other) you would need to look into implementing checkid_immediate
http://www.openid.net/specs/openid-authentication-2_0.html#anchor28