on earth: 究竟
How on earth did he do?
他到底是怎么搞的？

in order to: 为了
In order to complain about our business affairs?
就是为了听你抱怨公务的事吗?
I came here for years in order to paint.
我来这里多年是为了绘画.

live on one’s own: 独立生活
As an emancipated minor, Andrew would be able to live on his own.
作为一个脱离监管的未成年人Andrew将独立生活。

release from: 脱离
This medicine will give you release from pain.
这药吃后会解除你的疼痛.
He had won his first release from the fences of home.
他第一次成功地脱出家庭的樊笼.