I happened to have the same problem but not to the extent that it's killing our server or flooding me (postmaster) with email.
What you need to do is look at the headers and figure out if the spammers are using some system that is an open relay or not. If they are, calling or emailing the postmaster of that server may help to remove the problem.
Getting the hundreds of email from irate folks about spam - nothing can be done unless you just want to filter them and not do anything. The problem with that - one: your company does not look good in the eyes of potential customers; two: you will never get rid of the problem.
Yes, it is probably impossible to stop spammers one email at a time but finding the problem children on the internet (the open relays the spammers are using) or complaining to their ISP (those who are selling them a piece of a subnet) will help.
Check the headers - they will lead you to the folks involved. Complain to the postmaster, hostmaster, abuse, any contact person in either ARIN or NetworkSolutions database for that IP or domain name.
Check out
Network Abuse Clearinghouse for further info.
If you are just a user looking to get rid this mail, then a filter would work.