If you do not say on what city of China you are located, it is difficult to steer you to a place to buy what you wish.  Any of the larger supermarket chains have a section with foreign food, parmasan cheese from Kraft is normally there, as well as many other goodies like pasta sauces.  We have at my city three western food stores, expensive like hell, but still manage to get a few things not found otherwise.  Some will not shop there because of prices, I do go and look around, and sometimes I do find good bargains.  But really look at expiration dates, local store owners pay no attention to them, and keep expired merchandise on shelves until they are sold.

Go to the one on the corner. 

Try Carrefour.  They have a few in Qingdao.
You can also buy Kraft singles at almost any larger supermarket...it's not that good, but it will ease your cheese fix in a pinch.
http://www.echinacities.com/qingdao/listing/carrefour.html

Try Metro in Sifang.

Try Walmart they have almost everything you need...if your someone who likes to eat in and not eat out a lot go try Walmart....