ITG-3205 help understanding data

The first thing I would do is integrate the readings and display the integrated version - should be much clearer to see if its doing the right thing.

What is the full scale sensitivity and the number of bits - you may find the readings are quite small and the noise is making the signal hard to see (this is why you should integrate or low-pass filter). Gyros in general won't be sensitive to knocks unless the knock turns the sensor so it does sound a bit suspicious but do realise the noise will easily mask the signal for low rates of turn (compared to full scale).