Nasty things, tree rats. They kept uprooting my Double Eagle hedychium, I finally had to pot it to keep them from killing it.
Okay, environmental issues aside, use moth balls. It works until the rains melt them away and then you have to reapply.
No flaming please, everyone has to do what's right for their situation. At least I don't trade kudzu and water hyacinth and it's very plentiful in my area.

I'm having a problem with iguanas! Maybe we could have your squirrels and my iguanas fight in a death match.

I have had problems with squirrels, too. I would invest in a pellet gun and practice your head shots. If you can find a nest, destroy it immediately (or they will destroy your house finding materials to add to the nest)!

Another option is to get a dog for the backyard.

Well it really had nothing to do with gingers! But we had been looking for 3 years for a dog, and right on my birthday I found her.....her squirrel chasing is limited as we just keep playing and petting her!