Multiple aliases with single login
If you want a simple solution I can suggest what I did before is to redirect both domain.org and domain.net to domain.com using .htaccess redirect rule then all users will be reffered to domain.com first and then log in once there.

You need something like that in .htaccess (or simillar in your httpd configuration file):

RewriteCond %{HTTP_HOST} ^(www\.)?domain\.com [NC]
RewriteRule ^(.*)\.html$ http://domain.com/$1.html [R=301,L]


Or do you need more complex set up and have separate 3 domains with single sign on ?
Then try to use Domain Access module (http://drupal.org/project/domain).