If I need to ask someone about their birth order, what question is usually used? Let's say I do not ask how many children his family has first.
What is your birth order? or Which child are you in your family?
FTR I'm going to go ahead an give you a useful answer, which I believe is correct.
There is no good phrase for that in English.
Quite simply, it's one of those things in English where we all know there's no good clear phrase for it -- what you normally do is bumbling out something such as "So, like, you have older brothers - sisters I mean - or young or what, were you the oldest, youngest, or in between?" or something like "where do you fit in your family, oldest, youngest or?" ("Fitting in" with your family is confusing as it has other connotations, but you sometimes hear that.)
There's just no good clear way to say it.
Note that the many many many tediously linked answers contain ...... not one good suggestion. Not scientific proof, but a excellent pointer that, in fact, there's no such term here.
It's extremely important to remember that the "no" answer to SWRs is, uhh, very important - and you should remember that.
I would normally ask "How many older siblings do you have?"