Like Vicky, A.J.'s last name is unknown. Also, it's unknown what his initials, A.J. stand for.
He is generally assumed to be African-American.
One of A.J.'s ancestors settled in Dimmsdale Flats and he was an inventor and genius in its own right.
He once tried to buy the internet.
While A.J.'s family is obviously well off, he is not considered among the popular kids, possibly because of his high intelligence and because of his friendship with Timmy and Chester.
Crash Nebula is his favorite Super-Hero, as showed in Sleepover and Over. But in Smarty Pants he says that he doesn't know anything about Crash Nebula. However A.J. may have started liking Crash Nebula at some point between Smarty Pants and Sleepover and Over since Smarty Pants came before Sleepover and Over.