Is there such a thing as free storage while on deployment?

There are storage options depending on where you reside. Each situation is different. If you live off post and are not receiving BAH, likely not. If you live in the barracks your unit has the responsibility. If you are authorized off post housing and single likely yes. You need to speak to your S1 and the transportation office. Your unit should also know these answers based on its deployment order.

I know I was reimbursed for my car storage while overseas. And my belongings were stored for me at a nearby naval base.

Yes, it’s called a conex!

All jokes aside, when I deployed the unit offered household goods storage. Y’all to your command, you may be able to work something out.