I agree with the others
And start writing everything down like a timed journal of good days bad days, what he ate, times he started acting up and then you can look for trigger patterns.
Also be consistent and make the punishment fit the crime. Don't keep trying different methods like this hasn't worked and I have been doing it for a month now because it will confuse him more. He needs to see consistency from you to learn to be consistent.
When you say NO don't change it or bargain with him.
If he has food allergies here are two good books
The Crazymakers by Carol Simontachhi
And Brain Allergies by Dr Philpott
Also some are linking lack of Omega fatty acid in kids to behavior and thinking
All About Kids: Omega-3 fatty acid and kids brain health