Set up your local-host-names file (probably /etc/mail/local-host-names) with one domain per line, as such:
Unlike making changes to aliases or the virtusertable, you must restart Sendmail to load in the local-host-names file, as such:
kill -HUP `head -1 /var/run/sendmail.pid`
The DNS entries for your domains must have an MX record for your mail server as well, so if you do your own DNS, edit each domain's zone file with an appropriate MX record, as such:
Hope that helps.