Shuddering for you cos I'm an introvert too and while I love entertaining and hospitality I couldn't cope with days upon days of relatives! They just have to ....go.....home.
My strategies would be:
Meal plans: I'd try and serve food that won't spoil if people don't all come promptly to the table. Stuff like soup and brown bread for lunch so people can help themselves without it taking over your kitchen. Stews, curries could sit in a big pot, or slow cooker. And they can be made ahead and frozen so all you have to do is defrost and heat up. Those kind of dishes actually taste better when the flavours have time to merge. And it doesn't have to be samey - a Normandy pork casserole one day, a hearty boeuf bourguinon, chicken chasseur, a simple spaghetti bolognese. Keep breakfast simple with cereals, toast and juice.
Personally I'd aim to keep people out of my fridge but this is largely because I'm a control freak and I don't cope well with discovering that someone has eaten the Parma ham that was supposed to be the starter for Christmas Day and the cream has gone off because someone forgot to put it back in the fridge after the late night hot chocolate.
Ask the children's parents for food suggestions and be as specific as possible. Kids can be funny about brands and it makes life easier all round to cater to their whims in the short term.
while I think it makes lots of sense to ask people to do specific jobs and bring specific items my relatives have form for half doing the job and forgetting what they promised to bring. If you're cool and can roll with that then there's no problem but it would drive me demented. So I'd rather take responsibility for the lot myself.
And being an introvert I'm perfectly happy to do all the prep and cooking if everyone else would go for a walk as a previous poster mentioned. catering for a crowd is just a bit of extra work but organising jobs for people and delegating and waiting while someone chops the onions oh so slowly would be exhausting!
Go through your serving dishes, pots and pans and think about what you'll use each one for, with a packet of post its to label them if necessary. I have a habit of mentally assigning the same pan to two different dishes if I'm not careful.
You might need to switch on the dishwasher after each meal even if it's not completely full in order to make sure you don't run short for the next meal.
And schedule in time for yourself, even if it's just to lock yourself in the bathroom for a few minutes and check in with us on mumsnet