Update:
I've been doing a little digging on this.
If you are using AT&T, call them.
When you get a customer service person on the line, ask them to look up article 446389 in their system.
That document gives them instructions on how to block all SMS and MMS messages sent to your number that originate from an email address instead of a phone number or short code.
Note that if you rely on things like notification systems that send you SMS messages, and they come from email addresses, this will prevent you from getting them.
I'm in IT and have several notification systems I rely on that do this. I'm in the process of investigating alternatives so that I can stop the new wave of spam messages coming in.
If you're with another carrier, call them. See if they can do the same thing.