Please check your Mail server relay settings. You may want to run relay test from http://www.abuse.net/relay.html. As far as I know you can't restrict the From Address to any user. But the original point is to deny such users to use your mail server to send mails and for this you need to check relay thing.
It's not particularly useful yet, but it won't hurt to set up SPF and Microsoft "Caller ID for Mail" TXT records for your domain. Then AOL, Hotmail, and few others will refuse the mail in the first place, knowing it's not from you.
If you use a default catch-all then try disabling that until the flood slows some, that can help too as then some remote MTA's will refuse to accept from the spammer.
Basically you need to make it as difficult as possible for the spammer to send using your domain name, having SPF and no default catch-all means there's more of a chance their garbage will get blocked and they are less likely to use your domain then