What is the difference between 不管， 不在乎， 不理 , 无所谓 ?

不管：
(a) not care. Ex: 我不管你是谁。你不能进来。→ I don't care who you are. You can't get in.
(b) no matter. Ex: 不管我说什麽，他都不听。→ No matter what I say, he won't listen.
(c) Literally, not deal with. But other possible English translations could be "not take care of" and "not pay attention to", and it has the idea of "letting sb have their own way". Ex: 据说 Brad Pitt 和 Angelina Jolie 现在都不管他们领养的小孩了。→ It's said that Brad Pitt and Angelina Jolie now just let their adopted children have their own way.

不在乎：
can not care less; can't be bothered

不理：
Literally, "not handle". But can be extended into "not respond" or "not get involved".
Ex: 他正专心在看电视，门铃响了他也不理。→ He was focusing on watching TV and didn't respond to the door bell.
Ex: 我不理你了。→ I'm done getting involved in your business.

无所谓：
(a) not matter. Ex: 他想要救父亲的命，花再多的钱都无所谓。→ He wants to save his father's life and it doesn't matter if it's going to cost him.
(b) be not the point; be not about sth. Ex: 我就是喜欢练身体，无所谓减不减肥的。→ I just like working out. Losing weight is not the point/It's not about losing weight.

我不管 = I don't care (what happened/what is happening/whatever trouble you'll/you'd go(ne) through).
我不管了 = I'm done dealing with/paying attention to it.
我不在乎 = I can't care less/don't give a shit. I can't be bothered.
我无所谓 = It doesn't matter to me.