I once heard about Jewish aggada telling about big bird throwing huge eggs made of steel which were destroying towns. Does anyone knows if there such aggada exists and what the source for it is?
You seem to be looking for the Bar Yuchnei. Talmud Bechoros 56b:
The gemara there says that normally this wouldn't happen, but this particular egg was rotten so the bird threw it away.
It seems that there is another Jewish bird of such proportions called the ziz. Wikipedia quotes a book which attributes this gemara to the ziz; it seems that this might be a mistake of that author, or perhaps the birds are one and the same.