When talking to Justin Cole over the phone, Starfire mentions a "death in the family". This is a reference to comic book storyline Batman: A Death in the Family which depicted the murder of Jason Todd by Joker. The storyline was originally published in September thru November of 1988.
Reference is made to a street named Blue Bird Way. In the comics Bluebird is the vigilante alias of Harper Row, a member of the Bat-Family.
Red Hood says, "You know the tune, outnumbered, outmanned," referencing lyrics from the song Right-Hand Man, from the Broadway musical, Hamilton.
Scarecrow's quotation, "Home again, home again, jiggety-jig" is from a traditional English nursery rhyme called "To Market, To Market", that dates back to the 1500's.