Hello and welcome Skinman.
Draining the pond won't ensure the end of the duckweed. Once drained, the pond bottom would have to be either thoroughly frozen, baked in the sun, or treated with herbicide. It only takes a few surviving DW plantlets to start another infestation.
It's normal to have some foul-smelling sediment in older ponds, even without runoff from fertilized fields. Unless the water always stays very green with little visibility, the fertilized fields probably aren't harmful.
If you don't mind, I would like to know what kind of fish you find when the pond is emptied.
Good luck,
