Good guesses, but I think that rye is pretty close to looking like wheat with the seed at the top of the stalk. I think oats have a more leafy look to them. If I had seen these alone rather than in acres by the hundreds, my guess would have been that it was something you'd only find at a florist shop as filler.
Here's another one:
Headed out there tomorrow, so maybe will take a few other closeups and/or get a sample.