Hello. Sounds very familiar. My son is now 16, and seems to be settling down, but he has been haaaard work. I think some kids are just more 'difficult' than others, and when they reach adolescence they go through a few years of being truly horrible. As a parent, you just have to hunker down and hang on in there.
School WAS part of the problem for my son - he did no work and got into trouble a lot and generally found it very stressful... But as soon as he could see the light at the end of the tunnel (around the start of this year) he relaxed a bit. He's doing GCSEs now, and may get a few of them, and is applying for construction apprenticeships with a place on a level 1 joinery course as a fall-back.
Basically he just wants me off his back, and the more I can manage that, the easier things are. I have told him I will support him in whatever he does so long as it's work or study, but I won't support him dossing around on the dole. I have to tolerate things some I don't like - like tobacco and cannabis smoking - but not in my house. It's a compromise, but it works, mostly. He's stopped swearing at me and stealing from me.
For me, it helped to stop trying to work out 'why' he was behaving the way he did, and just be clear about my responses to it. I found in the end, it didn't really matter whether he was stealing because he was disturbed, angry, mentally ill, or just plain bad... I just wanted it to stop: so I started to hide my purse from him so it wasn't possible. Similarly, it didn't matter why he was getting into trouble at school - whether he was bad or unhappy or misunderstood - Rather, it helped to ask him whether he wanted to be getting into trouble, and then to help him remember what he must DO or NOT DO if he wanted to stay out of trouble. We had a lot of conversations that ran along the lines of "But it wasn't my fault, s/he made me do it" (him), "But DID you do it?" (me), "Well, yes, but s/he made me" (him), "Well if you did it, then that's why you're in trouble; you'll just have to deal with it" (me), "But it's not fair" (him), "It doesn't matter whether it's fair. Schools aren't always fair. It's the RULES, You just have to deal with it".... Then leaving him to deal with it...
The hardest thing for me has been recognising my lack of control (he made it pretty clear to me the last time I grounded him - he was about 14 - when he just laughed at me and climbed out of the window). I have had to come to terms with the fact that I am NOT in control of all sorts of aspects of his behaviour and choices - and he will fight me if I try - but I AM in control of my own behaviour, reactions, safety, and most aspects of my home environment.
It sounds callous. Maybe it is. But it's practical. He wanted independence, and I was resisting it, always stepping in to try and 'help' or 'sort things out'. I WAS 'banging my head against a brick wall' (as you said). So I stopped.
I don't mean I stopped caring, or talking. I always talk to him, and you never stop caring, do you?! But I stopped trying to DO things and SORT things. And it has helped. I think he felt I was treating him like a 'problem' and he was probably right. He didn't like it. Now I try to find as many occasions as possible where i ask HIM for help... I don't always get it, of course, but the number of time I DO is growing pretty quickly - from abou 5% to 50% over the past 2-3 months, I'd say. Last week he fixed our broken toilet seat, took the bins out AND vac-ed the living room and stairs!
I think he wants to grow up, and has been really frustrated and furious that the world won't let him. Maybe your son is the same.
It's soooo hard when they're 14, because they really ARE still your responsibility, and children, even if they don't want to be. As they get older it DOES get a bit easier, honest! Good luck!