Weeds in small grains are THE biggest problem for organic growers. It's a big reason to plant winter wheat in September (in very well cultivated and weed-free-at-present ground)... you will have many fewer weeds sprout in the cool and short days of fall, but winter wheat grows until the ground freezes, which lets it get ahead of the weeds.
Oats need to be planted as early in the Spring as possible... again, because they sprout and grow well in cool soil, but many of the most aggressive annual weeds don't really take off until it starts to warm up... a 4 week "head start" for the grain is huge in terms of final results.
As you mentioned, if you needed the food, it could be salvaged. As nuts as it sounds, I've found it can actually save time overall with very weedy grain (but which still produced decent, full heads) to just go out with sharp pruners or snips and large pails and harvest by cutting the heads off the grain. Tedious and time consuming, yes... but the amount of time and effort you save in cleaning trash and weed seeds out of the grain is significant.
If you have chickens or other livestock, you just harvest the field, weeds and all. Dry it like you do when harvesting the straw, then bed pens with it. Cattle, horses, hogs and poultry will all pick out much of the grain (and poultry will eat a lot of the weed seeds as well), and then the straw provides bedding.
We have a fairly weedy, late planted oat field we grew for bedding which is nearly ripe. We'll be cutting and baling it soon... the trick is to not wait until it's perfectly ripe, as the baling process tends to thresh out a lot of the grain. If it's cut just slightly green (barely out of the dough stage) the grain stays attached to the straw, and isn't wasted.
Summerthyme