I've added a player to the 'admin' group and given him moderatorid but he is still unable to use any oxide commands, he gets a warning message in chat saying he doesn't have permission to use the command (eg o.load pluginname). How to I allow him access to do this, or is it an owner-only thing?

Yes, they would still need permissions.

oxide.grant group admin oxide.*

or individually based on the full matching permission name. The only time permissions are not needed is via rcon or server console.

Also make sure they log off and back on after you give them the moderatorid..