Well, in the nicest possible way - you are making a choice. You are choosing between a range of shitty options. It would be great if choices were horrible thing v great thing. But often they're horrible thing number 1 v horrible thing number 2
. such is life. you just have to choose which horrible thing you're going to go for 
One of your choices is to pack a bag and leave. Give him a massive shock and hope that he realises just how strongly you feel about it. This is not the same as leaving the relationship. He just has to think it is. You may call it 'games', I call it a clear demonstration of strength of feeling 
Another choice is to stay on strike. Cook for yourself, wash up only what you need, when you need it. Do nothing else. Accept that this means you live in a pigsty.
Yet another choice is to hire a cleaner to come in every day. (this may only be a choice if you have the money!)
One more choice is to throw away anything left on the floor. so clothes etc. In the bin.
Another choice is to not to his ironing and just leave it in a heap.
Buy cards and gifts for your relatives but not for his. Make sure they know that he really couldn't be arsed. (a variation on this would be to buy them something and sign it from you alone.)
Don't be his calendar. If he expects you to remind him when things are happening - don't.
don't be his clock. If he won't get up - leave him to sleep.
Whatever you do though, it has to hurt him and not you. So not doing any ironing - you're going to cave in. Just don't do HIS and if you can ignore the pile of his clothes in the corner of the room, you can keep that up for the rest of your life.
Not doing any dishes - if you don't do any, then as you've discovered, you soon have nothing to eat from. If when you want to eat (the single meal that you are cooking for you, because of course, you aren't cooking for him any more!) you wash the single plate, knife and fork you need and the pots you need to cook with, and leave everything else - again - hits him but you get to eat.
you say he won't take any responsibility for anything. Why is this? Is it because all things household are, he feels, your job? Is it because he is childish? Is it because he lacks confidence? Is it because he's a lazy arse who thinks you're there to service him.
Knowing WHY he behaves the way he does is the key to change.
One thing is as sure as hell though - if you carry on with your life the way it is now, you will grow to loathe him. He needs to understand this.