You have two options; one, lie on your ESTA questions...saying yes will automatically get you declined. Or two, not bother with the ESTA and go straight to your embassy. I would advise you not to lie on an ESTA. They can (and do) gain information about any passenger on that plane and even if they didn't, when you go through immigration they grill you. I've known people be turned away, and I've known people be kept for hours sweating, to finally be let in. Do you want the stress of worrying or do you want to get that visa in your hand?
My husband has a visa because he has a caution (not even a conviction) for common assault (on his brother, when they were 18). He is now in his 40s, never been in trouble since but that is still relevant in their eyes.
My advice is don't go to the US Embassy for advice, because they will tell you to get a visa, because to them it means $$$. You need a subject access form from the police and that will tell you what history he has (you'll need this later for an interview anyway). Customs and Border Protection are nothing to do with the US Embassy and their advice is inaccurate. But, if you go to C&B, they will tell mention Crimes of Moral Turpitude and the person in the OP definitely has convictions related to these. They don't like drugs.
Take your chances by all means, you could say nothing and get away with it. Or, he could be turned away at immigration and sent back on the plane he came in on. On a 15k holiday I wasn't about to take the risk for the sake of getting a visa. In our case though border control huffed and puffed because we didn't need one...they said if it was drugs that would have been a different story.
That said, I've also known plenty to be turned down for a visa at the interview, especially when it's drug related. In that case you can be automatically turned down, see you later, don't ask again...or you could apply for a waiver, and they take MONTHS to come back. So if you decide to go for the visa I would do it pronto.