If the bales are still in good shape so that someone else could use them, place them on the curb with a sign that says FREE. If not picked up in a couple days, be a good neighbor and dispose of them this next way.
Properly prepare the material for yardwaste collection. Because the bales are likely too heavy, you will need to break apart the bales of straw for collection. Put the straw in paper yardwaste bags, or loose in a trash can.