in the config.php try changing $CFG-> wwwroot to something like below
$CFG->wwwroot = 'http://' . $_SERVER['HTTP_HOST'] . '/moodle';
the $_SERVER['HTTP_HOST'] should let you access moodle from multi domain names to IP addresses.
WARNING certain things save actual IP address or yoursite.com into the database. and you may need to do a "migration" thing on the database. see http://docs.moole.org and search for "migration" for more information.