I would confine this hen to small safe area to closely observe, and make sure she has feed and water..
see if she eats and improves.
also watch for any other symptoms.
please describe the messy vent..what color is the mess?(important)
check her crop...after she eats it should feel full.
in the morning before she eats it should be empty or flat.
check for lumps, a grainy feeling, or any sour odor.
check the belly/vent area for any swelling or heat.
has she ever laid soft shelled eggs?
does she feel thin?
it's possible she could have eaten something bad..either toxic plant, or something treated with a chemical, or something dead, rotten with maggots..or even stagnant water.
I'd try giving her some plain active culture yogurt with the oatmeal.
and vitamins might help..
no veggies or corn until her droppings improve.
I'd also up her protein.
has she been wormed?
if so when? and what was used?
has she been treated for mites?