Are we talking about straw bales normal harvested or about special compressed strawbales ? to build a two story house?
Yes, normal straw bales though you want the baler set to make them as compressed as possible.
My timber log cabin one story 3.7 meter high (gable ) 2.8 meter walls ) shrinked about 30 -40mm already , hope thats all

, but what happens to the plasterwork if a house shrinks ?
The usual technique is to "pre-compress" the walls with tie-downs (wire or plastic tape) before putting the roof on. Yes, they do settle a bit more and the plasterwork goes on fairly late in the process.
Yes you can make straw bales loadbearing but youve still got to protect the straw from rodents and damp. Rodents seem to be able to smell a source of food and chew through most non metal building materials.
The straw itself is basically woody material so pretty much inedible though it'd be good for nesting, I suppose.
As Billi points out, settlement / shrinkage is inevitable, which means you have to design flexibility into the structural openings. So a gap might be required between lintels and windows to allow the walls to settle onto the windows, cos the alternative isnt pretty and a very flexible waterproof render is required. I dont think lime mortars will stop damp ( they actually look to keep cob walls damp )
As I understand it lime mortars work fine to protect straw.
So not sure how you might create a long term building if the straw has to be structural ?
There are 100 year old load bearing straw bale houses in Nebraska - hence load bearing is called "Nebraska style".
Be interested to learn how it is done.
I'd recommend "Building with Straw Bales: A practical guide for the UK and Ireland" by Barbara Jones. A first place to look, though, is her company's web site:
http://www.amazonails.org.uk/.
I was interested in the idea for a while though I think the plastering is more labour intensive than anything I'd want to try to tackle. The whole thing can get a bit fraught with weather and keeping bales dry as the roof and plaster goes on.