I have a storage room with a lock on it. I try to wrap as soon as I buy it, or while the kids are at school. One year I paid someone to take them to the movies so I could wrap. Sometimes we wrap while they are asleep. Rather than putting names on the presents (just in case one of the nosey buggars get my keys) I use a different color sticky dot for each child. This way if they do find it, they dont know who it is for. As far as disguising your handwriting, print Christmas labels on the computer.
Before we had the storage room I stored at a relatives house...very inconvienient on Christmas Eve though.