Like a phoenix, a firebird is a bird that is perpetually on fire, providing it with a natural attack and defense superior to that of more mundane fowl.
Real World References
Firebird was an automobile released by Pontiac between 1967 and 2002.
The Firebird appears in real world Russian folk tales where it is often the object of a difficult quest, fitting in with Ceasar Borgata's difficult quest to take back the city of Chocula from Carpool. The same mythical bird is also the subject of a Stravinsky ballet.
Being 'birds' they fit the theme of Transylvito units being slang terms for women (along with Goyles, Dolls, and Molls.)