Divine 'aha' one oddly struck? Beats me! (1,4,2,4)

I believe the answer is:

i have no idea

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'divine aha' is the definition.
I know nothing about this answer so I can't tell whether it can be defined by this definition.

'one oddly struck? beats me' is the wordplay.
I cannot really see how this works, but
an anagram of 'one' is 'eno' which is located in the answer.
'me' could be 'i' and 'i' is present in the answer.
This may be the basis of clue (or it may be nonsense).

Can you help me to learn more?

I've seen this clue in the Sydney Morning Herald.

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