These three phrases can be used to express emotions and feelings that cannot be controlled.
For example in the following sentences:
1) How do the above sentences differ? Are they all interchangeable? Are any "stronger" than the others? (To me てたまらない seems particularly strong due to たまらない meaning "unbearable".)
2) If we were to literally translate the above sentences would they be something along the lines of:
a) I lost by one point, it's so frustrating it just can't be.
b) I lost by one point, it's so frustrating there is nothing I can do.
c) I lost by one point, it's so frustrating it's unbearable.
Note: I understand the てならない and てしょうがない have an additional function when used with verbs which can mean "can't help but", as in この写真を見ると、子供の頃のことが思い出されてならない／しょうがいない。However, for the scope of this question, I think we should keep it to the meaning of "unbearably" or "so ~".