This is very unnatural to say - it's a pleonasm, too. One would say "Hvilke fødselsdagsgaver fik du" or "Hvilke gaver fik du på din fødselsdag".
I can see how it's redundant, but when I first saw this it was nice to see a direct connection between fødselsdagsgaver and its component parts.
The hvilke seems very weird - has there been a mixup of birthday gifts so our hero must pick out the ones which are rightfully his?
According to other comments hvad + noun is wrong Danish, it must always be hvilken/hvilket/hvilke + noun.
Instead of "which birthday presents did you get....", Can you say "which birthday presents have you recieved...."?