I hope my translations help you understand the subtle different

nuances though I don't make sure it is 100 percent  correct in English translation

1.너는 가야 돼
I don't care others, but you should (must)go

2.너가(=니가) 가야 돼
You are the person to go because you are the right person

3.너도 가야 돼
You are also should go

4.너만 가야 돼
You definitely should go alone

5.너부터 가야 돼
Don't say others, you should go first

6.너라면 가야 돼
그 사람이라면 말해줄 수 있을거야
I think he could tell you something

7.너니까 가야 돼
8.너라서 가야 돼
Because of you (=It's you) so you should go

9.너 혼자 가야 돼
You should go by yourself

10.너를 (=널) 위해 가야 돼
You should go for yourself

11. 너 역시 가야 돼
You should go as well

12. 너 빼고 가야 돼
Except for you, everyone should go

13. 너랑 가야 돼
I have to go with you