Mine are ND as well, which is why I try to make it only a weekly nag session, rather than daily. I’ve found that I leave it, it gets out of control and then they feel overwhelmed - and it makes their ADHD/ASD worse - so I try to break the cycle each week. I will start to clean it up ‘with them’ (bring the laundry basket in, bring a bin bag and the hoover up). Strangely they tend to be grateful afterwards and I’ve found they are gradually getting into the habit of tidying up more often. The ADHD etc means they procrastinate/lose track of time, get absorbed in homework/gaming/books and don’t realise that although they meant to do it, they’ve run out of time. So although your son is 17 (mine are 19 and 16, clever etc) he may still need some support and gentle structure/guidance.
Re your DH - I find my DH goes through phases of being a bit of an arse with them - bit of work stress spilling over, worries over bills/job that makes him a bit, well, wankery about the kids not looking after the stuff he provides etc. And unreasonable expectations, given the ASD/ADHD, in that he doesn’t really get it. I’m the expert, not him.
As others have said, I would talk to both separately - and ask them both to take a moment to consider how the other feels/what might be going on in their lives that makes them stressy/dickish (and, yes, it’s normal to be those things from time to time)… and ask them what they can do to make things easier for each other. Perhaps 30mins tidying his room together once a week would help, maybe the two of them going out for a beer one night a week, to connect as adult blokes outside the house?
It is really normal for two men to rub up against each other at this point - you’ve a young adult male in the house trying to work out where he fits now he’s no longer a kid, and - if anything like my kids - a weird mix of older/wiser for his years whilst also being incredibly young/naive. The ADHD makes this point of his life extra complicated. Rubbish to have to always be the negotiator and peacemaker, but if this fails - bang their heads together!