Why is rectified open circuit voltage much lower than with a load?
I rewound the secondary of a 850 watt microwave oven transformer (MOT)
  so the open circuit voltage (OCV) after rectified by a full bridge
  rectifier is 14.4 volts.


OK, that's a peak voltage of about 22.6 volts: -



Your meter reads the average voltage (when set to DC) and that is 0.636 times the peak voltage.

When a moderate load is applied, that peak voltage will drop to about 21.2 volts. This drop is due to the forward volt drop of the diodes in the bridge rectifier.

So you connect this to a 12V lead-acid battery and you need to take care here because you are exceeding the charge voltage limits (usully about 15 volts for a deep charge). But ignoring your ignorance and assuming that you only did this for a few seconds to take your reading, it should not be surprising what is happening.

Your original reading was 14.4 volts and now, with the battery it reads 17 or 18 volts - this is because there can be no voltage returning to zero volts in the rectified waveform - it returns to maybe 13 volts (i.e. the car battery voltage) so now your average reading is somewhere between 13 volts and 21 volts. That sounds about right if you read 17 volts.

Be very careful about what you are doing here - do not leave the 12V battery connected to this output - it is dangerous.