兄貴 = Aniki is mainly used by males and used, when talking about your own older brother
兄さん = (o)Nii-san without the "o" is also used for your own brother, when directly adressing him, when saying "onii-san", you mostly speak of someone else's older brother
弟 = Otouto is used for "little brother", as in, when you introduce your little brother to others (Watashi no otouto desu = This is my younger brother), using otouto-san, you always speak of someone else's little brother
兄弟 = Kyoudai means in general "brothers and sisters", not only "brothers".
There is, from what I know, another word for saying "older brother", which is very outdated and definitely not said anymore by anyone these days. It is a very honorable way of saying "older brother".
兄上 = Aniue