In theory, if you have 80 or 160 ppm of nitrate and you change 25% of the water and add water with 0 nitrate you should end up with 60 or 120 ppm. This assumes you test a short time after you have added back the water.
So all the possibilities that make sense to me are pointing towards the readings are not accurate (tester error would be included here). Unless you have a pretty high KH, persistently high nitrate results in some amount of nitric acid which could lower your tank's pH. Of course, in well buffered water you wont see this in a week.
The signs of nitrate poisoning are the same as they would be for nitrite. However, nitrate has a very difficult time passing across the gills into the bloodstream due the its size. It is similar the NH3 being able to (why it is so toxic to fish) and NH4 being too big and thus unable to. Unfortunately some can get in and when elevate nitrates are present, eventually you will see the symptoms. So if your fish are not at the surface gasping, they are not in immediate danger.
Gross overfeeding should leave a lot of gross looking mushy stuff in a tank and/or cause a bacterial bloom, so it probably isn't that?
I agree with eagle that things don't add up and I am sticking with not trusting the results for whatever reason. But to be sure, test the tank, change 50% and retest after the refill. If you don't see a clear big drop, I rest my case ;-)
