go to the local liquor store and grab some boxes. those survive the shipping from France and Argentina, they should survive a move around this country.
You may want to think more along the lines of how the wine is packed when you receive it in the mail from a winery. Each bottle is nestled in a form fitted cardboard cushion and packed in a sturdy box to prevent crushing (see image). If you can't pick up these somewhere, you could buy some heavy duty boxes and bubble-wrap from a hardware store and pack them in tightly to prevent them moving around.
I would avoid making them too heavy and risking the movers dropping them or roughly setting the down. Maybe 6 bottles per box then? This also limits your risk in case one is dropped.
Also watch the temperature of the moving van if possible. It is not likely they will be subjected to under 25'F temps and freeze at this point of the year, but they still could overheat and push corks.
A little pricey, but depending on what you are moving, it may be worth it. This company has a few options, including the picture that jgmillr1 posted. Here is a link to one. Search wine boxes and you will get other options.