Hi,
Interesting ... We have worms which seem to be identical. Ours turn in to tiny green flies and are apparently harmless. We have had them for ages, no one seems to know what they are or how to get rid of them.
Our fish are also Goldfish but interesting enough, if we need to medicate the water, we usually increase the salt content (using aquarium salt) which seems to get rid of the flies. A few months later and they are with us again.
In our case it doesn't seem to be linked to water quality or overfeeding. The fish don't seem to mind (they don't eat the flies or the eggs) so we don't mind either. Would like to know what they are though.
TTFN,
Pog.