Does he have any brothers ? If not, then you don't say either (youngest or oldest son). You would just describe him as 'THE son of ..." or that he is the 'ONLY son of ...' if you want people to know he has no brothers. If he has brothers, then it depends ... If he is the oldest or youngest brother, then you say that he is the oldest or the youngest son, whatever is the case. If he has one brother older, then you can say he is the '2nd oldest son'.

US: Youngest and eldest really isn't important very much and is *especially* unimportant when you're talking about twins. If you are the only children, you'd say "we're twins." If there are other children, you would say "we're the youngest" or "we're the oldest" or "we're in the middle" depending on whether the other children are older or younger.

You would both be the eldest children (your parents eldest son and eldest daughter), as long as there are no other siblings in the family. It would be very strange for age to be used when referring to either of you though, since you are twins.