Yes, I caught my fair share of eels this fall on the St Croix.. I think everyone can agree on that..
What to do with them? #1, dont take them in an aluminum boat with no carpet.. they get some speed going if they cut the line, or fall off the hook. It will be a memorable occasion when your passengers panic! (That can be good or bad, depends on the passenger )
The easiest thing to do is grab the hook with a pliers and shake them off the hook unless they have swallowed it.
Some people eat them, and have asked me to keep them if I get them again. I guess they taste great, I dont know, and dont know if I would want to experience cleaning one.. killing them isnt all that easy either if you are using your spotlight to bash it on the bottom of the boat, they seem uneffected.
I would like to see how these things stand up in captivity. A 5 gallon bucet with a lid might make it out fishing with me next year so I can transport one or two to a local(to the eel spot), covered bullhead tank Brian K can give me a call and let me know how its holding up