It's better to sell it and buy yourself new furniture wherever you go. Put a good, cheap price on it and put it all on craigslist or something similar in your area. If you don't sell it, you'll either have to move it yourself or hire someone to do it for you, and they won't be cheap, because it's a pain to move stuff, especially if stairs are involved. Have a giant yard sale and get rid of all you can before you go.
How do you move furniture? You physically pick it up and then place it in the new location.. DUH.
So I'm having a garage sale soon because we're moving and want to get rid of everything. But how do I move furnature or how else can I sell it?