There have been a number of batters who have adopted unusual batting stances or routines. I'm not sure how "quirky" that is, but:
was known as "Bucketfoot Al" for his unusual stance, which had his front foot pointed down the third base line (or, in baseball parlance, with his "foot in the bucket"). A few other batters have since emulated his style, but none so successfully: Simmons is a Hall-of-Famer.
Willie Stargell swung his bat in a strange, windmill-like fashion two or three times before every pitch, and then jerked his left arm up and down a couple of times. He's in the Hall of Fame as well.
Perhaps the goofiest character ever to play the game was Mark "The Bird" Fidrych. He won 19 games in his rookie season with Detroit while engaging in much strange behavior, including talking to the ball before pitching to the batter. He developed arm problems after that season and his career fizzled out not long afterward.
, a mediocre pitcher for the Senators, later developed a comedy act that played in baseball parks for decades after his retirement from the game in 1921. In this he was much like Max Patkin, the "clown prince of baseball," except that Patkin never played in the major leagues.
Many of baseball's "characters" were best known for their antics off the field: Tug McGraw, brothers Dizzy and Daffy Dean, Charlie "Jolly Cholly" Grimm, Jose Cardenal, Bill "Spaceman" Lee. In the nineteenth and early twentieth century, many of the most colorful characters were, in truth, hopeless alcoholics: Michael "Turkey Mike" Donlin, Bugs Raymond, Rabbit Maranville, Rube Waddell, and even Babe Ruth. Nowadays folks don't think drunks are nearly as funny as they used to.
: I'm in the left field bleachers. Can't you see me waving?