Using menu tokens (or similar?) to create "invite user link" on OG Group page I am new to tokens but was planning to use the menu to token to create a simple menu allowing group administrators to easily invite users without going to the Group administration menu.

The default Organic Groups (7.2x) link for inviting members is: http://www.example.org/group/node/GID/admin/people/invite-users

As the Group ID (GID) is the same as the Node ID (NID) I thought that the [current-page:url:args] would work well. so I created a menu link with the path

group/node/[current-page:url:args]/admin/people/invite-users

Which crashes all group pages and also makes it impossible to delete the link in the menu as "the website suffered a temporary issues". Uninstalling the Menu token modules solves the issue but I am wondering how to make the menu link work as I intended.

For anyone interested in the bug this seem to be a known issue (see: https://www.drupal.org/node/1205086).
I was having similar trouble as you, due to the bug in menu-token.

The way I would go about is, as a work-around, is to create a views-block relative to your groups, adding your node id or gid as a field that is not displayed (you'll have to move this to the top of your fields list in views for it to work). 

Then you add a "global text" -field with a value like "Invite", re-writing the output as a link that includes the node id/gid as a token in the URL. This must be located below the node id/gid in the field order(!).

Finally, you will have to set your views filter to restrict the output to the page a user is currently on, this way the Node id/gid field will return only the correct value. Also set your pager to a single result as measure of ensuring only one value is passed through.

Hope this helped!