The NuSOAP server for eZ publish currently uses the default siteaccess (just like the default soap server of eZ publish).
What do you have in settings/override/site.ini.append(.php)? This should make site1 the default access:
[SiteSettings]
DefaultAccess=site1
Did you activate the nusoap extension for site1 (or for all sites, that should work too)?
Now for your virtual host configuration. I guess you're using name based virtual hosts instead of IP based vhosts? Just like you did with your other vhost configs, choose a name for it, eg. soapsite1.mycomputer.mydomain.com, and use this after the ServerName directive.
If you can't get it to work, then please post the vhost config for the soap server.
For setting up rewrite rules, see: http://ez.no/doc/ez_publish/technical_manual/3_6/installation/virtual_host_setup You can use this to have soap.something.com as a virtualhost with nusoap.php
