Using straw for anything that is loaded in flexure will be a disaster. Reinforced concrete theory relies on the reinforcing to act as a crack stopping mechanism which will yield in a ductile manner. Straw's variable strength and inability to place it at critical sections means that it cannot perform the function of reinforcement as it will be possible to encounter localized weak reinforcement which will not prevent cracking and loss of section leading to progressive and sudden failure.
From my own experience, I saw that wood rots quickly for about 1cm (1/2") when it contacts with concrete or cement stucco, but remains intact when enclosed in cement-lime mix. IMHO, lime is important to save wood/straw from rotting.