What are harmful levels? Your tank is indeed overstocked and I would be quite suprised if the
NO3 (or other nitrogens) where not at elevated levels.
In regard to the eels problem, it may be "plugged up", hard to be sure. You should definately skip the fish from it's diet. The fatty tissues are not the best thing for it and can lead to this issue especially if
FW feeders. Stick to crustacean flesh for the most part and try to sneek in some veggie matter occationally. Feeding should be about 2x a week and feed until the eel is satiated.
I would in the mean time suggest several large water changes with well aged/aerated
SW. It can often do wonders where no immediate cure is available. I think it's just a matter of wait and see but please post you water quality numbers as soon as possible.
Cheers
Steve