Asmodeus is the name given to the "Prince Of Demons" in Abrahamic religions. He supposedly personifies lust.
The young lady that appears in Artemus' magic trick at the very end in addition to being James' "engagement" also seemed to be an inside joke. Who was she.
Astarte is another name for Ishtar, the Mesopotamian goddess of war and fertility.
A month after this episode originally aired, Anton Lavey founded the Church Of Satan in San Francisco. There is speculation that Lavey based his look - shaved head and Van Dyke beard - on Asmodeus.
According to John Wayne's character in "Hondo," Astarte is an Apache name that means morning with all the sensations that accompany it.