A little would depend on the circumstances, Hirashin.
Normally (b) would be the only possibility:
(b) If I had been born in 1982, I would be over thirty.
In the usual classification of conditionals this is a mixed 3rd (past perfect in the if-clause)/2nd (conditional in the main clause) sentence.
Such a sentence is appropriate for occasions where we are contrasting an imagined or real event in the past with the present result of that event - the event in the past is my birth, its present result is my being over thirty. So that works well.
(a) If I were born in 1982, I would be over thirty is a conventional 2nd conditional. 2nd conditional sentences are used when we wish to talk about imaginary, hypothetical or unreal situations, and the results consequent on this imaginary situation.
It's hard to imagine circumstances in which (a) would work. If a lot of angels were lounging around in heaven, sometime before 1982, wondering when would be a good time to be born, one might say If I were born in 1982, I would be over thirty in 2014, but without the in 2014, either explicit or understood, I can't see how the sentence could work.
So, for me, only (a) is an idiomatic sentence in normal circumstances.