Organic Groups strict membership access I have set up multiple organic groups on my site that can only be joined with admin approval.

My issue now is that members can post content in groups of which they are not members. I really don't want this.

Does anyone know of a module or technique to stop unauthorized members from posting content in a group but only in groups they are members of and hence authorized to do so?
You need to enable Organic groups access control module. This will let you set your groups to public/private.

There is a tutorial series on Organic Groups which explains everything you need to know about the configuration at http://modulesunraveled.com/organic-groups