Does the body have any significance? Does it have some personal value, or is it something hard to find? The reason I ask is it would probably be cheaper to buy a strat body already painted. You can get them from different places online. Warmouth is expensive but they do a great job. They charge anywhere from $180 for an unfinished alder body to $225 for walnut. Then you will want them to paint and finish it. That will cost another $180 to $220 and we aren't even talking about sanding off the old finish. I'm fairly sure they don't do re-finish jobs. It might be cost effective if you did all the work yourself, but if you really want a nice job done to it you'll either need to know how and have the tools, or have it done by someone else and that won't be cheap. Here's an example....

http://gmvintagerestorations.com/prices.html