The comic takes a lot of inspiration by part of English folk musician Kate Rusby. Tom is a fan of her.
Sir Eglamore, ("Sir Eglamore") the Annan Waters ("Annan Waters") and Janet Llanwellyn, ("The Maid of Llanwellyn") all take their inspiration from several of her songs. Tom also Title Drops Awkward Annie in The Rant on one of his pages, which is the name of one of Rusby's songs/albums.
Reynardine's name (and his initial encounter with Annie) are inspired by the traditional song "Reynardine", which Anne covered.
Winsbury is from the traditional song "Willie O' Winsbury" (interestingly, Kate Rusby also recorded a variant of this song, titled "John Barbury"). In the song, Willie is in a relationship with the king's daughter, Janet, much to the king's displeasure. Replace "king" with "headmaster" and ... yeah.
Lindsey & Bud's names, and the fact that they're engineers in an underwater habitat, to The Abyss.
Reynardine and Ysengrin are heavily influnenced by Reynard and Ysegrim from Reynard the Fox.
Tom called Lily "Cookie Monster" when he named her in a tweet. She also shares his color scheme and seemingly has toned-down mannerisms and speech patters of Cookie Monster.
The random patch of skin and hair (Robot's arm seems to have neither) could be a reference to Star Trek: First Contact, wherein Data the android gets a "skin graft" that starts out as a square inch of skin and hair.
Chapter 59, "Jeanne": Annie's plan to free Jeanne is basically to do an Inception: the blue-haired fairy is the "architect" creating an imaginary Court for Jeanne to live in and populating it with literally Faceless Masses while helping Parley, the "forger", play the part of Jeanne's dear friend. Annie and Smitty are both "extractors" — Annie, with Kat's help, is going after the mysterious green arrow that killed Jeanne's boyfriend and locked Jeanne's spirit in the gorge while Smitty's powers combined with Parley's ensures that everyone can *bip* in and out safely. Red is there for... moral support.