how do I create multiple domains and manage more than one organization through the Nuxeo? Or do I need to deploy a Nuxeo distribution for each company?
If your question is multi-tenant, I try to give you a wide view on this subject here: http://answers.nuxeo.com/questions/855/multi-domain-isolation-for-users-documents-workflows
In Nuxeo, Domains are just documents so if you log in as Administrator, you'll be able to create new Domain document. Just get here http://yourserver:8080/nuxeo/nxpath/default@view_domains or click on the breadcrumb icon.