I am trying to find in Repetier's code the tables in which temperature control is located for both the bed and the extruder.  I am studying the Solidoodle as part of an internship and my mentor wants me to try and figure out how to control these temperatures a little more finitely (i.e. so they don't oscillate so much).

Repetier has no such tables.

Repetier feeds simple commands to the printer, on the order of "Set this temperature x"

The printer then attempts that temperature.

The communication is accomplished via gcode. http://reprap.org/wiki/G-code
You will need the above page, more or less in entirety if you plan on understanding the printer.

The *firmware* of the printer does have thermistor tables. However, that is most likely not what you're after. We provide firmware sources at www.solidoodle.com (search firmware). You can edit the tables and recompile the firmware with the tools we provide.

Usually, we *reduce* the oscillations by running a PID algorithm. The above document explains this.  M303  is the command you are looking for. This should help, but some oscillation is normal with these printers.