打烊: generally for inns and small restaurants, which is a more northern, local way of expression and carries a longer history than the other two (though I haven't used it for quite some time): e.g. 这家餐馆打烊了。
关门 is used broadly, but it can also mean "closed for good," not just for a short period of time, so the exact meaning has to be determined by the context.
so is 营业,which is a formal way of expression and used for more modern kind of business (supermarket, convenience stores, restaurants, etc.).
btw, shops and stores sometimes put up signs-"开始营业“ ("Open") and "停止营业” /"营业结束)(“Closed")