Hay is well known for its radiation blocking properties
It might be dumbed down; but assuming you don't have concrete block or lead shielding, getting a couple of feet of soil between you and the blast is about the best way to reduce exposure to the initial radiation.Then if you consider that soil is primarily decayed plant material... Hay isn't exactly a nonsensical material to line the walls of a barn with.
Soil is dense, hay is dry grass in bales. I'm pretty sure that would do nothing to help.
Shielding: The term 'biological shield' refers to a mass of absorbing material placed around a reactor, or other radioactive source, to reduce the radiation to a level safe for humans.[1] The effectiveness of a material as a biological shield is related to its cross-section for scattering and absorption, and to a first approximation is proportional to the total mass of material per unit area interposed along the line of sight between the radiation source and the region to be protected. Hence, shielding strength or "thickness" is conventionally measured in units of g/cm2. The radiation that manages to get through falls exponentially with the thickness of the shield. In x-ray facilities, the plaster on the rooms with the x-ray generator contains barium sulfate and the operators stay behind a leaded glass screen and wear lead aprons. Almost any material can act as a shield from gamma or x-rays if used in sufficient amounts.
http://en.wikipedia.org/wiki/Radiation_protectionIncluding materials such as water and wood--which are listed under the section "Shielding Design."
Notice how it says its determined by g/cm, hay is pretty much the lightest material possible and would be useless for shielding. Sure anything can be used, if you had a mile of hay it might help but I doubt a few bales will do anything. Remember this is the same people that sad hiding under a desk can protect from nukes.
Ok well next time a nuke goes off go stand in an outhouse and let me know how well you are protected.