I'm not sure whether these answers are 100% correct, but I hope they help.
Academic English = usually taught at school/university/college level; includes English used in textbooks, prescribed literature/poetry books, etc.
Business English = used in the workplace; phrases that are not commonly used in casual English conversation, such as, 'service level agreements', 'productivity rate', or 'appetite for spending', etc.
General English = what you are taught when you are learning to read and write English for the first time, eg. correct grammar, sentence structure, spelling, punctuation, etc.
I hope this helps :)