the nitrite will be a killer, while the nitrate is sky high most fish can cope with levels around that.
i think there's two possibilities for what has happened here
first possibility is that the tank is part way through cycling, you may have over cleaned the filter killed off the filter bacteria and started a cycle, you may have missed the ammonia spike but are now experiencing the nitrite spike, this would account for the high nitrates.
second possibility is that the nitrite is being created because of dying plant, fish or decaying food in the tank, this would create high nitrates but i'm not sure if they would get that high.
few questions to help decipher what's happened, please try and give as much information as possible, even small details that you may not think are important may be critical.
what sort of test kit are you using, what make and model, is it a liquid test? How old is the test kit?
please describe exactly what you do to maintain the filter each week?
what is the filter, make and model?
what species of plec is it (please get a photo if you don't know) and how big is he currently?
how much food to you give the fish and what sort?