Wrap as you go. You don't want to be overwhelmed and overstressed Christmas eve.
wrap them as you go along then your family are left in anxiety about there presents.
I find it way too tiring to save it all for one night. I prefer to either do it as I get the gifts, or at least spread it out over a few days.
I do it now. I've been up till 3am wrapping presents only to have the kids wake up at 5am.
Then your mission is clear.