I take “quirky” to mean characters that are odd, who act in unexpected ways, are a bit peculiar or different, maybe a bit outrageous or unusual in some way. They’re the type of character that makes a book either very good or boringly bad. It really depends on the situation and whether they fit into the story or are there just for effect.
There are so many characters that can be described as quirky but one that came to my mind as I read the question is Alice in Pinkerton’s Sister by Peter Rushforth. She is certainly eccentric and peculiar, nothing she does is what people expect of her. The book starts off: “The madwoman in the attic was standing at the window.”
Her neighbours think she is simple, strange and definitely mad and are outraged by what she says and does. It’s a bizarre story mainly seen through Alice’s mind which because she lives mainly in the world of books is a very strange place indeed. It’s funny, well ludicrous at times, full of literary and musical references and I got lost in it for hours.