Thanks to JJ, there are 4 new struts on the car and now I can drive over bumps without feeling like I'm on a carnival ride or something.
Ordered 4 Gabriel Readymount struts from Autozone. It's the complete strut including spring, so all we needed to do was take the old ones out and replace them with the new ones.
Installing them wasn't nearly as difficult as I expected, although we did have to disassemble part of the back seat to get at the bolts for the rear struts.
Ran into problems getting the wheels off because of cross-threaded nuts. Ended up having to break off a bolt on three of the wheels. Going to have to talk to the guys at Treadquarters about that, since they were the last ones to take the tires off when I had it in for an oil change and tire rotation a few weeks ago.
Car rides a lot better now. Need to get the alignment checked now in case anything changed with the new struts.