Genesis 38:8 says, "Then Judah said to Onan, 'Sleep with your brother's wife and fulfill your duty to her as a brother-in-law to raise up offspring for your brother.'"
Archer is not surprised that Ray is not a fan of the Old Testament, most probably because of passages such as Leviticus 20:13 which advocate putting two men who lay with each other to death. These types of verses are frequently cited by religious groups who are against homosexuality.
When Ray says he's going to beat his brother like a rented mule, Archer says that that sounds like something from the Bible. Numbers 22:21-32 contains a passage about Balak beating a donkey three times (a mule is the offspring of a male donkey and a female horse) only to have God chastise him for it, by speaking through the donkey's mouth.
Randy's direction to "slap iron" to any wounds recieved in the shootout is a reference to "The Outlaw Josey Wales."
Archer comments "For all we know, they're building a Gundam suit with bazookas for hands", talking about the burglars having broken into the ISIS armoury. This implies Archer has some knowledge of semi-obscure Japanese culture.
Kenny Rogers Roasters is a chain of chicken based restaurants founded by country musician Kenny Rogers and former Kentucky governor John Y. Brown, Jr.. Cheryl thinks a rooster is a chicken, then when Ray corrects her and says it's a rooster, she thinks it's a Kenny Rogers Roosters; Ray has to correct her again.
Sheriff E.Z. Ponder used to tease Ray for wearing capezios in high school; Capezio is the trade name of Capezio Ballet Makers Inc., a manufacturer of dance shoes, apparel and accessories.