The band sings "Monster Mash" in the beginning and ending of this episode, which is set in 1960, but "Monster Mash" was not a hit until 1962.
Richie refers to the ritual as an "exorcism." Before the 1973 movie came out, exorcisms were a fairly obscure ritual known only in the Catholic Church. It is unlikely that Richie (the Cunninghams appear to belong to a mainline Protestant church) would know that term in the late 50s/early 60s.