"New user registration by invitation only." -- Possible to make option where invited users still have to be approved?

hm, you could combine with logintoboggan module:

create a role pre-authenticated user and use this role fore invited users, then aprove the invited users with this role.
(and it's up to you which rights you give to pre-authenticated - this is a role between anonymous and authenticated)

Just in case anyone else reaches this page in search for mentioned feature. There is a hook_invite available in this module. That can be used as below to Keep invited registrations blocked resulting in Admin approval in both direct and invitation registrations.

// hook_invite implementation to undone account activation on registration by invitation by Invite module
function mymodule_invite($op, $args) {
  switch ($op) {
    case 'escalate':
      db_query("UPDATE {users} SET status = 0 WHERE uid = %d", $args['invitee']->uid);
    break;
  }
}

Tajinder Singh
IMP Technologies
Creating Masterpieces...
http://imptechs.com

Thanks for this helpful tip TajinderSingh. You saved my day :)