Are the Japanese names of the characters from Ente Isla references to something? I feel like there is some kind of joke with the characters' fake names that I am missing.

One of the characters I think asks if their names are outdated. Is that the joke, just that they are using archaic names? Or is there something else?
If you're asking what "the joke" is with names like "Maou Sadao" and "Yusa Emi", the joke is that their Japanese names sound suspiciously similar to their Ente Isla names/titles:


"Maou Sadao" is very close to "Maou Satan" / "Demon Lord Satan"
"Yusa Emi" is very close to "Yuusha Emi" / "Hero Emi"
"Ashiya (Shirou)" is sort of close to "Alciel" (Arushieru)
"Urushihara (Hanzou)" is sort of close to "Lucifer" (Rushiferu)


As a side effect of this, some of their Japanese names sound curious/archaic, since you kind of have to stretch to find Japanese names that sound similar to Christian angel/devil names.

Separately, some of the names are also "translation jokes", so to speak:


The "Suzu" (鈴) in "Kamazuki Suzuno" means "bell". Indeed, her Ente Isla name is "Crestia Bell".