There could be several causes to this but you will need to start with the easier and more obvious solutions. First, does your ear speaker work? That's the one for making phone calls.
If it does, then you'll want to focus on the Lightning Port and Loud Speaker. It could be that the loud speaker pins where damaged or misaligned but because the Headphone don't work either, I would suspect that the Lightning Port flex may have been damaged. You can try and replace it yourself by following this [guide|62572|guide]. It's not the easiest DIY repair so go through the guide first to see if you're up to it.
If that doesn't work, then the issue could be on the logic board. The impact could have damaged some tiny solder connections. This will require that it be looked at by a micro-solderer.