So sorry that you are having such a troubling experience! And you are right- it sure sounds like more then ADHD. Some questions I had while reading:
What have the counselors said about the lack of empathy towards others?
When caught stealing, how does your son feel about his behavior?
When stealing, how does that make him feel? Can he identify his emotional state while stealing or binge eating?
Does he remember doing these things? I ask this because I had a moment when I was 17 and was entrusted with a position at my work where I was handling large amounts of money. I started stealing from my employer and although I knew what I was doing, the knowledge was vague after I justified it to myself. I do not remember single instances, just that it was 'something I did that one time'. That one time turned out to be way more then even I realized. Yes, I got caught, charged, and convicted.
What I'm getting at is that, even to this day, I can't remember the acts, I just remember that I felt a little more okay with the world- a little more secure- but also felt dirty and wrong and like a bad person. It's hard to keep feeling this conflict, especially if you feel it's part of who you are and can't change your 'wrongness'.
Just throwing this out there- intellectually, he knows those things are not "correct" behavior, so he knows he is "wrong". Having a sense of shame around his impulses while not feeling like he can control them could set be setting him up for some pretty nasty internal turmoil. Stands to reason that a young brain would shut off painful emotions with that kind of assault on its person. Hence the rage and self-victimization.
Do you suppose there's any merit to trying to emotionally de-charge the situation and come at it from a purely intellectual pov? As in, identify a moment when its occurring, add no emotion just come at it from a neutral position (ie, stealing is socially unacceptable and does not allow our society to function well in its presence, so let's deal with that. Make it right by giving it back. No extra attention paid to the act about it's right or wrong). Let him add the emotion... which it sounds he will do without much prompting other then calling him out on the original behavior.
When he does, listen. Listen until he runs out of words. Those words might hurt you or be really hard to hear. Empathize with him anyway. What you hear as crazy extremes- you felt that at some time in your life. It sucks to feel that way, right? It might just throw him off enough to start to see himself in a different light. Maybe not, but it might spark an awareness in him that he can share what he's feeling without being reprimanded for those 'wrong' feelings. Feelings aren't wrong, they just are. Separate those from his actions.
The lack of empathy is concerning, though. If you feel that you or your other children (or any others for that matter) are in physical danger, please don't hesitate to get help!
Again, so sorry to hear about your challenging situation and I hope you find the solutions you need! Much love and energy sent your way!