Origin of pronunciation of "er" as "oi"

It is a Brooklyn, NY regional accent you are hearing in the cartoons and in the Three Stooges. Moe, Curly and Shemp Howard (all brothers) were born and raised in Brooklyn:

"Moe Howard was born on June 19, 1897, in Bensonhurst, New York, a small Jewish community on the outskirts of Brooklyn. Moe’s real name was Moses Horwitz. Moe’s mother’s name was Jennie Horwitz, and his father was clothing cutter Solomon Horwitz. Moe was the fourth eldest of five Howard brothers. Two of Moe’s brothers, Jerome (Curly), and Shemp performed with him as members of The Three Stooges."

"Curly Howard’s real name was Jerome Lester Horwitz. He was born to Jenny and Solomon Horwitz on October 22, 1903 in Bath Beach, a summer resort in a section of Brooklyn. He was the fifth and youngest of the five Horwitz brothers. "

"Shemp was born Samuel Horwitz in Brooklyn, New York on March 17, 1895. He acquired the name “Shemp” when his mother, with her broad European accent, would call him “Sam,” which sounded like “Shemp.” Shemp graduated from P.S. 163 in Brooklyn."

From: http://www.threestooges.com/cast/

As a young lad, I lived in Brooklyn and visit frequently.

A native of Bensonhurst pronounces it "Bensonhoist". A native Brooklynite pronounces Brooklyn "Booklin".

"Tree doity boids, a sittin' on da coib, a choipin and a boipin - tree doity boids." Don't know where this came from, but my Dad (born & raised in Brooklyn) used to recite it all the time.