(Especially the smell of smoked eel.)
I tried washing with soap, lemon juice, a metal spoon, but nothing really seems to work.
Washing with soap multiple times throughout the day will get it off eventually, but surely a better solution exists.
The fishy smell comes from amines - you want a low pH substance to take the smell away, like lemon juice or vinegar. Some brands of "shower cleaner" will do the trick.
Bicarbonate of soda absorbs "general" odors, but it is alkaline and not the best choice in this case.
Working in a restaurant and handling 50 to 60 raw fish a night the only thing I found to remove the smell was toothpaste. I put a small dab in my hands and rub it over front and back of hands and rinse. Fish smell gone. Never worked with eel.
While I've never had to deal with smoked eel, I like to make a thick paste of baking soda and water and scour my hands with it to remove odors that linger.
Hydrogen peroxide works, too. Just pour it straight out of the bottle..beware if you have cuts because it hurts! :)
I find lemon juice works well, or if you have a 'lemon flavour' washing liquid. I once did use mechanics hand cleaning stuff which was also lemon based. Worked brilliantly, but can't remember what it was called.