I stored my fabric in plastic bins and had no problems. I just recently bought a cabinet for fabric so I can see what I have. I like this method better & will try the ruler method for folding. Buying boards is way above my budget as I have many small pieces.

I too have used plastic tubs to store fabric. I too had trouble with the odor in the fabric. I don't think the tubs smelled very much, but a closed plastic tub has problems. Here near Houston it is hot and damp. Then I stored my fabric (in my family room--no space left) and I had the metal shelving that you can get at Home Depot or Lowes. I got large baskets and placed them on their sides, the open end facing the room. Then I stacked the fabric by color in the baskets. Well, I needed more space! My kids go to college, and I get the littlest room in the house, Yea! So I use the shelves, with Elna shelves below. I have 4 sets of them and they are metal mesh. I get air circulation, and can easily access the fabric. The upper part where the top of the shelves (metal)I have all sorts of supplies, orphan blocks, etc. stored there. I have on top of the shelves some of the large baskets, filled with yarn, quilt tops, and so on.
I have found that the problem with wood is that it is wood. The wood will bleed into the fabric if it isn't moved regularly. You may be able to line it and solve this problem. This has been the answer to my problem, but it also means that the room is pretty stuffed! I need to stop buying fabric or what ever until i use some of it up!

I was using plastic drawers and decorated cardboard boxes--and while I still have those tuck around the sewing room, I realized that most of my stuff was heaped in a corner in the sack it came home in and I never knew what I really had. So I bought a china cabinet at an auction--the lower part is solid doors that hide things like freezer paper, template plastic, some fusible, etc, and the upper part has nice glass doors that allow me to see what fabric I have for projects and still keep it dust free. It just seems so much nicer to work now. I do use plastic shelves for the scraps still without any problem.

I use clear plastic tubs with locking lids. I'm able to see what is in each tub while keeping out the dust, plus they stack well. I haven't noticed any plastic smell, but for those that have mentioned it try placing a dryer sheet in the tub and change as needed.

I found these directions for the Ruler Folding method - hope this helps:

http://turningturning.com/tutorial-folding-fabric/