Hey Oddgeir,
First, you can set your Joomla registration type to
`admin`, so that when the new user register on your site, they need to wait for your site admin approve it, then they only can login in your site.
Or you can disallow those new registration member do not have publish post permission from
backend > Easyblog > ACL > select your user group > publish entry - NO , once you set this permission to No, all the registration member submit their post in your site, they have to wait for your site admin approve the blog, then they post only will appear on your site.
Hope this will help.