How do I tell my site to ignore hits to dead links?

My site, WWW.misoenergy.org, is plagued by hits to the OLD URLs before we switched to Episerver. 

People wrote scripts, which for whatever reason they've never turned off that hit our hit day and night.

I know that exceptions and tracks down to controllers are SLOW actions. How do I tell my site to JUST IGNORE any request to those URLs? 

I don't want to redirect, just tell them to go away.