Self-oscillating inverter questions
Points to note: -


R1 and R2 set the base bias current for a BJT. All they do for a MOSFET is set a high gate voltage that causes a lot of current to be taken from the power supply rail.
The Base/emiiter region is a forward biased diode hence there is natural limiting of collector current due to BJTs being base fed via resistors
The forward volt drop at the base will be about 0.7 volt and any feedback winding voltage may enhance this a little or it may negate that voltage and turn the transistor off (this is what is needed) 
The feedback level may be nowhere near enough to turn off a MOSFET that is voltage biased on the gate at Vcc.
Circuits designed to work for a BJT nearly always don't work for a MOSFET


Try adding two resistors; one on each gate to the common source connection on your circuit. Guesstimate value: 150 ohms. If it stops oscillating then try 220 ohms.

If this doesn't work then try adding small value source resistors such as 10 ohms. If you can't get any of this working satisfactorily then try simulating the circuit and tweaking values in the sim.