Is there some way that one could control the three valves from one pin on the arduino?
sure, if you want all three valves to do the same thing.
Does there exist some kind of relay/transistor that can take let's say three different signals from the controller (for instance low, medium and high), and then relay the full 12v signal to the valve that correspond with that particular input signal?
I can't even imagine how that would work. But no, there's no such relay. You could build one with three relays and a microcontroller, but then why not just do it with the microcontroller you have.