Why do I still get some voltage at the load when the regulator supposedly is turned off?
Both the IRF4905
and the 2N7002 have a non-zero drain to source current when the gate to source potential is zero. For the IRF4095 the drain to source leakage current is 25 uA with a VDS=-55 V. 25 uA across the output load resistance of 903 Ohms (1 k || 9.4 k) gives 23 mV. This is reasonably similar to the 10 mV you measure, especially since the VDS is different than the datasheet and the VGS is not precisely 0. 
I can't explain why the node of the sampling divider is reading 0.04 V. I would expect that node to be 1/2 Vout (the op-amp has an input bias current of 5 pA).