This drives me nuts and I'm yet to meet one couple where the mental load is equally shared.
When I went back to work 4 days a week after maternity leave with DS1, I was clear things were going to be split. We do an online food shop once a week, which we alternate. Whoever does the food shop does the meal planning for us and DS for that week. A lot of things still fall to me though - booking DS doctor appointments, ordering prescriptions etc. Even all the stuff DH does around the house - he works hard to make our house lovely - I'm often reminding him to do it. Drives me nuts. I'm pregnant with DS2 and I've told him when he's born, we will take one child each. DH can be responsible for DS1's doctor appointments, school bag, nursery fees etc, and I will do the same for DS2. Divide and conquer, it's the only way it's fair, otherwise I'll end up having to remember it all. I'm sure there'll come a time when DS1 is sent to school with the wrong stuff, but if that's what it takes for DH to learn, so be it.
It's a bit late for you with the kids, but how much organising do teens need? If it's still a lot, I suggest taking the same approach, assign one child per parent. If one is sent to school without PE kit (surely teens should be able to take responsibility for that kind of thing) then it's dad's fault anyway, let them get mad at him. Take it in turns to food shop and meal plan. If that means take aways the week your husband is responsible, so be it. It won't last forever, he will get sick of takeaways every night and hopefully start pulling his finger out.
Family birthdays, I would ditch his family and only send cards/presents to yours. You've set a precedent here if you've always done it (I have never once gotten involved in organising cards and presents for in laws) so be clear with your husband that you'll no longer be doing it.
Divide the chores up clearly too. Assign him tasks eg hoovering, dishwasher unloading and make those solely his responsibility. If he doesn't do it, it doesn't get done. He'll soon notice when there are no clean dishes and the floors are disgusting. I do pretty much all the laundry, DH does all the hoovering. It works as it means it soon becomes obvious who's slacking when something's not done.
I've learned that clear boundaries between "jobs" is the only way for it to be fair, and you have to then just relinquish control and let the other get on with it.