I know you can do double-negatives in Turkish.

How would this be translated?

     I couldn´t not help him.

.

I´d say just make it "not helping him was not possible for me"

You can say it like that "Ona yardım etmemek mümkün değil."

 I couldn´t not help him. = Yardım edemedim değil

Yardım etmedim değil = It´s not that I didn´t help him

Gülmeden edemedim = I couldn´t help laughing at it

Hiç gitmedim değil = It´s not that I haven´t been there at all

This is a late reply but whatever, maybe you´ll read it. The best way to translate "I couldn´t not help him" is like this:

"Ona yardım etmeden duramadım." or "Ona yardım etmeden edemedim."

The form is "-meden edememek" but it has some other variations like "-mamazlık yapamadım/edemedim" (There might be more but I don´t remember right now).

Here are some other examples:

When he said it like that, I couldn´t not laugh. - "Onu öyle söyleyince gülmeden edemedim."

During the lecture, she couldn´t not sleep. - "Ders sırasında uyumadan edemedi."

Thankyou everyone.