I have a 2011 MacBook Air(11-inch), I am using OS X 10.9, but I only have 64GB Flash Storage, and I want to expand the storage of MacBook Air's hard disk. I asked geniuses at Apple and they told me the answer is no. So, is this possible?
It is possible, although not from Apple themselves.
A company called OWC seem to specialise in SSD upgrades for macbook's and have upgrades for your model available here
These particular upgrades offer greater speed and capacity to some of the stock apple SSD's from 2011.
I might also recommend you check out a micro USB drive. Kingston makes one called the DataTraveler micro. It's very small and only protrudes out from the computer a little. You can get them up to size 64GB currently.
You could also ad a Nifty Drive to your mac. You plug that in your SD-Card reader (which is used by that then). http://eu.theniftyminidrive.com
It is slower than an SSD, but you could move some stuff over there.