Sounds like a sensory issue, which can be part of ASD or ADHD but can also just be separate.
What you're describing is dysregulation, which means that he cannot naturally balance experiences he finds stressful with calming stimulus. That usually means that either this child is encountering more than usual that he finds stressful (where the sensory issues come in - assuming you haven't left out any whoppers like your DH is a violent alcoholic or something!) and/or doesn't have the tools/skills to self-regulate, or use parental input appropriately to help him regulate. Most likely both. That is why he cannot regulate his emotions or reactions and has such extreme responses several times a day.
Of course, it's totally normal for a 3yo to be partially unable to regulate their emotions and reactions - but to the extent you describe, and with the triggers you describe I think it probably is worth looking into. I didn't really understand this completely until DS1 (who struggles with all of this) was about 11, and his behaviour was unmanageable at 3. I now have a 19 month old and I'm astonished because his toddler behaviour is so completely different to DS1. For example, DS2 will sometimes display tantrum behaviour and you will catch him checking to see if you're watching him. He'll put on a crying performance, but forget to change his face so he still looks happy (and be able to switch it on and off at will to see what happens). Or he'll fall over and you'll see him actually take some deep breaths and then carry on as though he doesn't want to waste time being upset. When he was learning to crawl, he would rage with the effort he was making, but make a clear choice to continue despite that. If he knows something isn't allowed/approved of, you can see him thinking about it and deciding whether to do it or not, and fairly often he decides not. Of course, there are things which upset him, frustration he can't get past, incredibly tempting forbidden things and other emotional overload moments, he is a toddler after all, but there's a clear difference between these and the times where he is actually showing signs of being able to regulate his own behaviour to an extent. Obviously not very much, he is only little, but it is there and this is quite amazing to me, because I just assumed those were skills which developed later.
DS1 was nothing like any of those - he was regularly inconsolable, but I had no trouble following the attachment/gentle parenting advice to treat all tantrums as real and significant feelings because to him they absolutely were! I have no doubt that he wasn't being manipulative - he genuinely did find everything very overwhelming as a toddler. In fact, I was always a bit sceptical of people who claimed toddlers could be manipulative, and secretly thought they weren't being very empathetic
I had nothing to compare DS1 to, so no idea that he wasn't typical. I just thought his difficult behaviour was either me being crap, typical parenting advice being unempathetic, and so on.
I'd recommend a few resources to you:
On skills vs capacity:
The Explosive Child - and possibly Dr. Greene's newer book as well. This explains the skills vs capacity issue well. Dr. Greene has a website but I find it a bit confusing without the info in the book, it works well as a companion, though.
The Whole Brain Child/No Drama Discipline - just a brilliant primer to the skills vs capacity idea, v practical as well and suitable for your age range. Probably more universal than Explosive Child.
Smart But Scattered - he's a bit young for this to be relevant yet, but it's aimed at ages 4-14, so still worth a read. The best practical guide to improving the skills which are lagging (though it might be a bit advanced as yet.)
On sensory issues:
Too Fast, Too Bright, Too Loud, Too Tight - great book about sensory processing difficulties, explains how different sensory inputs affect somebody who struggles with them in comparison to how most people experience them.
The Highly Sensitive Child - not read this one, but it is meant to be good and along similar lines although I think Too Fast... is a bit more specific whereas HSC is a bit wishy-washy (but good and affirmative if you're looking for support). There is a quiz on the HSC website you can do for free.
On discipline/handling behaviour:
Janet Lansbury's RIE approach (website/book/podcasts) - good because children with these kinds of issues do not tend to respond well to typical parenting methods relying on sanctions and rewards to motivate behaviour - this tends to be overwhelming to them and/or if they don't have the skills, they can't do what you are asking anyway. However IME gentle parenting/attachment parenting is a bit too conflict avoidant, because these children need clear guidance and actually an overly conflict-avoidant approach can conversely be more stressful for them because it isn't always clear what your expectations are.
How to Talk.../How to Talk so Little Kids... - both good. I think the Little Kids one is probably slightly better at this age, it's also a bit more up to date although the books are extremely similar. So if you want the original, go for that. However, if you struggle to give boundaries or are a bit conflict avoidant by nature, go with Janet first, and this when you've got a handle on that.
Many of the above also have several websites/support pages on Facebook/in-depth reviews on the web, so if you don't want to dive in and buy a book, you can find an incredible amount of resources online.