Nothing to do but...

Here are a couple of 2kyuu grammar points that have similar
nuances. Out of all of these, I think しかない and なければならない are among the most commonly used out of the below. ざるを得ない and わけにはいかない sound a bit stuffy for me.
As for （より）ほかない, I don't know...

Ｖ + しかない : used in a situation where one has no choice but to do something.

Ｖneg + ざるを得ない : used in a situation where one has no choice but to do something.

Ｖneg + なければならない : used in a situation where one has to do something because s/he has an obligation to do it OR where one has no choice but to do something.

Ｖneg + わけに(は)いかない : used in a situation where one has to do something because s/he has an obligation to do it OR where one has no choice but to do something. It also expresses the unwillingness of the speaker to do Ｖ.

Ｖ/N + （より）ほかない: used in a situation where there is nothing else to do but X.