Hey Non-Science Guy,
The component names can vary but typically you will need a software package, pressure sensors, and data acquisition hardware to read the sensors. These parts are often packaged together in "systems." Tekscan makes pressure mapping systems that are very user friendly you can check them out here: http://www.tekscan.com/pressure-distribution-measurement-system
The data acquistion electronics connect directly into a USB port - easily portable! For applications like the one you've mentioned above the Tekscan sensors are ideal because they are dimensionally stable and won't compress when loads are applied, you'll be able to measure even slight un-evenness. The loads and sizes should be no problem for them.
Hope this helps.
PressureDude