Putting your old strings back once they were taken off is not a good idea if you ask me.

Have you ever tried to straightened a piece of metal once it was bent? It never comes back to it's original state. They same applies to strings. Once they were wrapped around the tuning pegs the tension and wrapping altered they original state, making them weaker.

My guess is that you'll have tuning problems and a lot more chances of them breaking off.

I wouldn't reuse them.