We're going to be staying at a villa a few miles outside of town and we need to drop our rental car off in the evening and then get back to the train station in time to catch an early train to Rome in the morning. Is there taxi service which will be available in the morning in time to get us to the station around 7am?
I've dropped off a car at Hertz in Orvieto and I do believe they have a key drop box. You'd have to verify that with Hertz, however. You may can drop the car early in the morning before getting on the train. I would suggest you run by that office late the day before and have them do a walk around on the car, however. I'd also take pictures of every inch of the car to document the condition.
There are a few taxis waiting at the station area; my experience is that the service may be patchy at odd times. Your best bet is reserve a taxi the day before; the municipal administration even publishes lists of available taxis and their phone numbers: