hakase=closest equivalent to the title Dr in japanese. Used a lot as Nii-hakase and Hwan-hakase in the actual TV shows.

aniki=older brother, elder brother. Used in context of Doku and Gojyo, since Doku truly is his respected older brother. Also used in crime family situations, or pretty much anywhere you'd have a mentor or someone to look up to, where a mentor or trusted comrade is also 'aniki'. Used only in the male context though. For a female it would be aneeki. Not to be confused with 'sempai' which refers to an upperclassmen, but used with the same amount of respect.

Hope it helps, others can give you better definitions than i. *prods Sychogrl*