How to use an 2-axis accelerometer as a potentiometer?
A quick-n-dirty way would be to convert your accelerometer's digital outputs to analog as shown in the data sheet at the bottom of page 5. Then you could use that voltage to inject current into an ordinary transistor (like 2N2222, et.al.)  That would cause the transistor to conduct more or less current depending on the voltage/current going into the base of the transistor. You could replace that 1K ohm "Fuzz" pot with your accelerometer-controlled transistor.  

The volume control would be a bit more tricky.  But you could use a similar "shunt" circuit to "short out" more or less of the audio output signal with another transistor connected like the "Fuzz" circuit.

A more proper method would be to use the digital outputs from the accelerometer into a microcontroller (Arduino, et.al.) and then use the microcontroller to control a couple of digital potentiometers which could be directly substituted in your circuit.