어쩌라고
This is one of the expressions that are difficult for me to translate into English.
It could be translated as “‘What do you want me to do” or “How do you want me do”.
ex) 너마저 떠나면 난 어쩌라고
If you are also leaving me, then what do you want me to do? (word for word translation)
If you are also leaving me, then what should I do? (IMO, more English-like translation)
어쩌다
This word has two meanings.
1) accidentally; casually; unexpectedly; by chance, by accident
ex) 어쩌다 나는 영화배우가 되었다.
I became a movie star by chance.
2) occasionally, once in a while, from time to time, now and then, at times
ex) 손님은 어쩌다 한 명씩 있을 뿐이다
We only have guests every once in a while.
어쩌면
This word also has two meanings.
1) how
ex) 어쩌면 그녀를 만날 수 있을까
How can I meet her?
2) possibly, probably, maybe, perhaps
ex) 어쩌면 그가 옳을지도 모른다
Possibly he is right. (He may be right.)
어쩔 수 없어
~ can’t help it.
ex) 일찍 떠나고 싶지 않지만 어쩔 수 없어.
I don't want to leave early, but it can't be helped.
어쩌나
What shall I do?
ex) 시험에 떨어지면 어쩌나.
If I fail in the exam, what shall I do?