Thank you, gokuyum. Translating songs is full of trouble for me. So, I have questions for you:
"Git ona söyle -- Go, tell him/her"
How do you know that it is "her" and not "him"? I am guessing -- obviously
-- but this song sounds like a jilted lover telling the girl to go her way, to go to the man she has chosen over the singer.
But you forget that I put this /
So I wanted to say it can be both 
"Ah gücüme gidiyor yalnızlığım böyle -- Ah, in this way, my loneliness offends me ( look at gücüne gitmek)"
I cannot find this phrase in my dictionaries. But I do find "gücendirmek" and "gücenme." İmdat!
Here is my favourite online dictionary 
http://www.sozluk.net/index.php?word=G%C3%BCc%C3%BCne+gitmek
"Ah bu inadından az mı ağladım ben -- Ah, have I cried a little because of your obstinancy? ( this sentence means I have cried a lot )"
I do not understand this. "Az" means "little," yes? And "mı" is the question particle, yes? So, is this a colloquialism that means the opposite of what it looks like? "I cried not a little because of your obstinancy." Anlat, lütfen.
Here with this question the person wants to tell that he/she cried a lot. But I guess you should be a native to understand this kind of usage. So dont worry and let it go 
And one last question: Is Turkish as filled with ambiguities for Turkish speakers as it is for English speakers? Of course, poetry nearly always has ambiguities -- it is supposed to make you think. But this question of "ay" seems very open-ended. For instance, does "moon bride" have a special meaning in Turkish?
Yes there are many ambiguties and word plays. It is one of the characteristics of classic eastern literature. It is sometimes like solving a puzzle.
Moon bride doesnt make sense in Turkish too
But in our poetry moon can symbolise the face of the beloved. For example ay yüzlüm ( my moon faced ) is an expression that you can see 
Thank you for putting up with all my questions. 