If you’re talking about store-bought or freshly baked challos on Friday that you want to stay fresh for the seudos on Shabbos day – so if they’re store-bought then yes, shrink-wrap them if you can. If not, then as soon as you get home – for home-baked, when they have cooled off somewhat but are still nice and warm – wrap them tightly all around in a few layers of plastic wrap, and freeze.
For leftover challah, as soon as you are finished eating the challah, wrap it as tightly as possible in a food storage bag, then twist-close (not tie) that in another food storage bag, and then in the freezer. Unless you eat challah with the soup, chicken, etc., just leave a slice on the table for bentching and wrap up the rest right after the fish.
In any case, the important thing is to get all the air out.