My electric water heater has had a steady trickle of steaming hot water coming from the overflo pipe for a few months.
We recently replaced the latco pressure relief valve? A black plastic UFO shaped thing on the outside of the roof? The next day the water heater started leaking badly from the T&P valve - we replaced that valve but there is still water leaking into the roof... it only happens late at night, and I haven't gone to see if it is actually leaking at the T&P valve or if it is leaking elsewhere... the heater does not leak if it is turned off at the breaker, and the water from the faucets seems very hot. Got any ideas?

Sounds like your thermastat is bad and the tank is overheating which causes over pressure. Have it checked. And whatever you do, do not plug the leak! This can cause serious damage and danger.