Spring plots might be tough if you don't have a way to control weeds. I do so by planting roundup ready soybeans. They will get eaten to the point of being killed and not produce much grain. But, it'll be a weed free slate to plant into this fall.
If the oats plots have a bit of bare soil now, I'd over/frost seed some clover into it ASAP. That would allow you to use a grass specific herbicide as well as mowing for maintenance.
Might want to look into using buckwheat. It's pretty good as smothering other things out and will only last 90days giving you something to plant into come fall.
A lot of suggestions might hinge on what type of equipment you have access to...
