Private WordPress blog, requires user registration approval, and allowing users to login with OpenID

Indeed, there is a way.

First, you’re going to want to install the Member Access plugin & the official OpenID plugin. Both of these are free

After configuring all of your pages and setting up the OpenID plugin, edit the robots.txt file in the WordPress installation directory. Add the following line:

User-Agent: * Disallow: / 

This will prevent crawlers from indexing your site, or discourage them at the very least.