Straw is what is left of the wheat plant after the combine harvests the grain. Unfortunately, a machine has never been designed that will capture all of the grain, so straw does contain some wheat seed. That is why your bales turned green.
Straw is an excellent mulch, or a good soil amendment when tilled in and let decompose in the soil. Yes, you may get some wheat sprouts and perhaps some weed seed with it, but you take that chance when you bring in organic matter from anywhere. I think straw is a good bargain for the gardener. When you cut the strings on those bales they just explode. There is a lot of organic matter compressed in that bale.
Around here most of the farmers have taken to using those big bales that they move with a tractor. I don't see many of the small "man-sized" bales any more.
Straw, as you learned, doesn't have much plant nutrition in it, and it is a poor animal feed too, so its main use is for bedding of animals. You will often find a lot of straw mixed with manure if the farmer uses straw for bedding. As with all plant matter, before straw can be utilized by the plants for nutrition, it must decompose. Use it for mulch or put it on in the fall and till it in.
Good experiment Tedlin.