If you haven't already read it, "Setting limits with your strong-willed child" is another excellent book for helping with managing challenging behaviour. I would highly recommend it.
Taking away his birthday party is an extreme measure that one wouldn't initially choose in response to a child's challenging behaviour, but it sounds like you've tried a lot of things leading up to this point, and this is a desperate last measure. You have also repeatedly informed him of this possible consequence and his behaviour has not improved. Making repeated empty threats as a parent disempowers you and also teaches him to not take your words seriously, so considering that he is still having a birthday celebration, just not the all-out, expensive party you were planning, I think it's important to follow through on the consequence that he was repeatedly made aware of. It's important, though, to not be a punitive parent, constantly punishing, shaming, and taking away, but it sounds like you're aware of the importance of not being like this. It's also important for consequences to be logically linked to behaviours, and I'm not sure taking away his birthday party is a logical consequence for repeated misbehaviour, but I suppose you could frame it in the context of a birthday party being an occasion where behaving well is important for it to be a happy event, and because he is not currently demonstrating that he can behave politely and respectfully, you are not willing to go ahead with a big party, but he has a chance for future birthdays. It's important to be calm and speak in your normal voice when telling him these consequences, rather than screaming and shouting, shaming, etc.
I have mainly read your responses rather than the whole thread, so don't know if this has already been said, but I wonder if him saying that he doesn't care about the consequences is just another step in the power struggle between you. I think he does care about these consequences, so I wouldn't worry too much about him saying he doesn't care. I think it is his way of trying to "win" the power struggle. The fact that he initially gets upset before saying such things supports that. I wouldn't take the "bait" when he says things like that. I think you just need to make sure that you're well-informed in the parenting approach you're taking, being firm, administering logical consequences for his misbehaviour that are not too excessive, whilst also encouraging him, showing unconditional love towards him, and making it clear that it's his behaviour and not him as a person that is of concern to you. You're doing everything you can, then, to help him to learn better behaviour.
No matter what he says, you are his parents and he loves you. I'm sure that deep down he cares about what you think, and you have more power than he might make you feel like you do.