We just started studying part-writing with four-voice textures in my theory class and since I don't have access to any suitable instruments I have no way to simulate these textures on my own, so does anyone know of any free computer programs that would allow me to input notes into a grand staff (with as many as four voices sounding at once) and have them played back to me with some decent tonal options?

Babya Logic is a pretty useful midi tool that would allow you to do that. The tonal quality will be that of a midi voice, and theres no ability to set the volume levels of the different notes, but it should get what you need done.

You can grab Noteworthy Composer. There's a free demo version, and the full version is inexpensive. You could also track down a tracker style program. Psycle is a fun one if you like synth timbres. I'm sure there is more suitable software too. Lilypond can be used to generate MIDI files, although they are nothing stellar.

I prefer a good synth sound to a poor emulation of a physical instrument myself. They have more life, since the way they sound is the way they are supposed to sound. If you have the chops, the best option for coming to grips with these sounds is probably to tap three of the notes and sing the last. Hearing a sound brought into the world by something other than a terrible-sounding computer piano really solidifies it for me.