Electronic stethoscope / contact mic not quite working
You clearly do not have enough gain.

In first attempt, you used MOSFET with V_gs(th) of 0.85 volt. This means the FET will not open at all as long as voltage is less than 0.85 volt. 

In your second attempt, you have connected high-impedance piezo output to input LM386, which has input resistance of 50K. This put way too much load on the piezo -- they like the loads of 100K to 10M.

I advice you either get a real jfet (mot a mostfet!), or put an op-amp such as TL081/741 in front of your audio amp.

And I recommend to add two diode protection circuit -- see http://www.openmusiclabs.com/learning/sensors/piezos/ . Otherwise, if you drop the device on the floor, piezo might generate so much voltage it will burn out the amplifier input.