Hard to know exactly what measurements you'd get.
I would get a voltmeter like this one:
http://www.ebay.com/itm/DC-150V-Ana...591?pt=LH_DefaultDomain_0&hash=item2a335ba967
With these "direct power" ones, they just have 2 connections on the back. I would put some sort of (stainless steel!) electrode at 2 ends of the tank, and when the eel discharges, see what kind of readings you get.
I know that the eels put out several hundred volts, but I suspect when you measure the voltage between 2 ends of the tank it will be quite a bit less.
Just having the volt meter would be kind of cool, but if you can narrow it down to that it typically measures 50 volts or whatever when the eel discharges, then you can build something more advanced.