Organizing help older house no storage. . . ?

I own an 1870's home with a lack of closets. Over the past few years, many things have been handed down to me, antiques and stuff that I love. Yet, I have no storage and my house is under renovation and I have to move stuff from room to room. I don't begrudge the beautiful antiques I have, I love them, but what do you do? With reno's and everything I am completely overwhelmed. How do I start? Where do I start? With the reno's dust is everywhere, I am embarred to have people in the house.