iMac is mysteriously unable to use WiFi that works for all other systems
It's not unknown for there to be incompatibilities between two things that are supposedly using the same WiFi standards especially since so many manufacturers departed from or anticipated the standards bodies in producing MIMO, draft-N (or even draft-G devices if you're dealing with something completely ancient). Is there an update available for your device? 

What you didn't say was what kind of access point you have in the house and what kind of wireless radios are in the PCs that work. You mentioned Airport but you might have meant the WiFi settings on the menu bar, or if you did mean it is an Apple Airport then it might be an original graphite UFO, a white UFO, an Express or an Extreme. I switched to a current model Airport Extreme (square) in the past year and found speeds and signal strength far better than my previous white UFO Airport Extreme.

Another thing to look at is what channel the AP is on. Are there any other access points visible from your house? You might be suffering from collision with a nearby radio and switching the channel in use in your house could help. This old blog fro New Zealand has a good illustration of how various channels overlap, so switching might be worth a try, even if the diagram doesn't seem to suggest you have a conflict.

Finally - can you just try moving the AP or the machine to see if things improve? It might look like there aren't any wireless obstacles between the AP and your machine, but you might find a thin wall houses a whole lot of copper pipes or foil insulation, and can be a fairly effective wireless shield.