I peel potatoes and leave them soaking in water in a pot on the stove. Although, I left them overnight in olive oil, with seasoning, in a Ziploc bag on Sunday night for last night and that worked well too.
I peel and chop the carrots and leave those soaking in water.
I peel the brussels sprouts, and leave those soaking in water. If they will be sliced before cooking, I only do that when I am cooking, not in advance.
Peel and chop parsnips and butternut squash, but put them in an airtight Tupperware tub (they don't soak).
Peel and chop the onions, put those in a separate air tight Tupperware (no water).
I make the stuffing in advance - I make breadcrumbs whenever I have leftover crusts etc and freeze those. Sometimes I even make a basic stuffing and freeze. Christmas stuffing is more seasoned, and DH adds sausage meat to it. But that can be done the day before (just make sure the meat has fully cooked and cooled before adding it to the rest).
I also make giblet stock for the gravy - just boil the carrot and onion peelings, some bay leaves, and the turkey bits, for a while, strain, and store in a pot on the stove or in a bottle in the fridge (depending on space). If you are super-organized, you could have that done beforehand and frozen.
If you have visitors and will need to do drinks, apart from having ice organized in advance (bag from shop or make lots of trays and empty those into a plastic bag or tub in freezer), I find it useful to slice and freeze lemon and lime in advance as well.