The Airport Extreme Base Station would be overkill. The less expensive Airport Express should be all you need. It is almost certainly the heavy walls that are attenuating your signal so in this case the physical distance is relatively immaterial.
There is some device in your home or in the area that is creating the noise you are seeing. Cordless phones, microwave ovens, fluorescent lights, electric motors, etc. are all electrical noise generators. Of course most of these are beyond your control.
Your results are not odd. It all has to do with the location and orientation of the antenna in each device. Often a difference of several inches can make a significant difference in received signal strength. It is the nature of the beast.
