I discovered that 1 of the relays under the passenger fender on my computer-controlled '81 has been lying under the battery tray and is totally corroded. I understand the 2 relays are for the TCC and the AIR/EGR systems. What do they actually do? I only have one working relay, which should I use it for (til I get a replacement)?

Well, with no torque converter lockup nothing really bad will happen except you will lose a little highway mileage. Not sure about the AIR/EGR thing, but I've never owned an 81. 80 without it and 82 (3rd gen), but never an 81.