When Strange is reading Through the Looking Glass and is coming up with a plan to create someone's backstory or persona it's a clear reference to a Batman villain, "The Mad Hatter" Dr Jervis Tetch who must be one of Strange's patients.
Jim makes a Jaws reference. When speaking to Barnes he says "We're gonna need a bigger gun".
In the comics Azrael is generally Batman's ally. Azrael himself is a modern day knight created and trained by The Order of Saint Dumas. In this story Theo Galavan (James Frain) is a descendant of the St Dumas. The first Azrael was Jean Paul-Valley and the second Micheal Lane, both Batman's allies with Valley even becoming Batman after his alleged death. It is possible that Gotham is using Galavan's Azrael as the characters first incarnation that will in turn leave him to rebuild The Order of St Dumas with him at the head. Eventually, Galavan would need to train a new Azrael, either Valley or Lane, in the future to kill the Batman.
Gordons "bigger gun" was a, Remington 870 outfitted with a drum mag.
The books Hugo Strange is choosing between are "King Arthur", "Tales from Shakespeare", "Through the Looking Glass and what Alice Found There", and "Alice's Adventures in Wonderland".