Cheryl refers to the Bechdel test. Created by cartoonist Alison Bechdel, the test is a measure of female representation; it is passed if a TV show or film features at least two named female characters who talk to each other about something other than a man.
When Archer mentions a SWAT team waiting to "go Attica", he is referring to the 1971 Attica Prison riot. When authorities stormed the prison to end the riot, over 30 inmates were killed, over 80 inmates injured, and 9 police officers were killed - all by gunshots fired by the rescuers.
Two of the clowns are named "Oingo" and "Boingo". Oingo Boingo was a popular L.A. based band in the 1980s and '90s led by Danny Elfman.