A.J.
This may be medical if: You firmly and calmly disciplined this from the very first times he tried any of these behaviors starting around 1 year old. Small tantrums, small defiance like running away when you called, all the small early stuff. You never let anything slide, but yet at 3, he's still doing all of it even worse.
But IF, you disciplined things sporadically or angrily after they had escalated (after age 2), and then gave up because he got even "worse" and "angrier" in those moments, this is totally normal and he's outlasting you with his difficult behavior.
Try six months (it should only take a week to see a big difference) where you remain calm and loving, but firmly dole a consequence EVERY TIME he does these things on the SECOND warning. During the beginning of a tantrum before it escalates, give one warning to cease, and give a consequence if he carries on. He may get po'ed and spin a larger tantrum in that moment (give him a minute to rage then calmly warn him to pipe down or continue the discipline) but after a few times where he sees the result is always the same and he's never allowed to carry out the fit without intervention, he'll stop at a warning. This will stop future tantrums, not always tantrums that are already happening. You want him crying because you gave him a consequence, not a self inflicted frenzy rage he feels like having.
At 3, he's well set in his ways so it may be a pretty big battle, but if after 6 months (max) of lots of love, attention, firm clear rules, discipline, plenty of sleep and healthy food, he's still completely out of control, have him checked out.
If dad's around, have him take the lead on discipline and attention and setting an example whenever possible, it's means a lot more to boys.
You said yourself you're not overly strict. It takes diligence. I have an easy girl, a very spirited boy, and a natural born terror beyond strong willed. I was very strict from the get go. They all caught on. Some quicker than others. Number three took diligence to a new level (early on before age 2), but she's great now. You can do it!