This is my elder brother's son.
elder brother哥哥。brother哥哥或者弟弟都行
This is my brother's son.
This is the son of my brother.
一般情况正常交流时,都不会刻意去用"elder"。除非有更进一步地问题,才会去解释是否elder brother or older than you.
(人在英国)
This is my elder brother's son.
This is my brother's son.