Feed the eel when it shows signs of being hungry, or as a base 2-3 times a week until full. You should be able to tell when the eel is full when it's sthomic begins to bulge. Regular feedings may prevent the eel being aggressive towards your fish, but the eel could still be aggressive towards your gobys because they occupy the same area of the tank.
In my opinion, I'd consider taking it to the lfs.
-prk543