I am new to PWM control. Is it advisable to operate a motor at higher than rated voltage with the "PWM average voltage" more than the nominal voltage specified in the datasheets? After some researching, the majority of the information that I kept seeing is that it should be OK (with a recommendation to operate at high PWM frequency). Secondly, if the "average PWM voltage" is kept less than the nominal voltage (with the supply voltage much higher) is it correct to refer to it as over-voltage operation? Or is it only when the average voltage is higher than nominal voltage?
As long as the PWM frequency is fast enough, it's average voltage is what counts. No, the average PWM voltage should not exceed the motor's rated voltage, at least not for long. This is no different that applying a DC voltage to the motor.
Using a high voltage supply and then less than 100% PWM to compensate is a perfectly legitimate way to run a motor, again, as long as the PWM freuqency is fast enough. In effect you are creating a switching power supply that converts the high voltage to the lower one used to drive the motor. It may not look that way because the induction of the motor widings are a integral part of this power supply.
It can be useful in controlling a motor to occasionally for short periods of time drive it with a higher than rated voltage. If using this kind of control scheme, care should be taken to guarantee that the overvoltage does not persist. You could go so far as measuring the temperature or calculating the energy dissipated by the motor along with the assumed decay to ambient to calculate the maximum drive you are allowed to apply at any instant.
You can't go too far with this. Generally 1.5x the specified drive voltage will be OK for short periods of time, especially when heating is taken into account. At higher voltages you will hit other limits, like arcing and insulation breakdown. Note that these apply to the peaks of the PWM waveform, not the average.
For example, a "5 V" motor run from 30 V with a PWM duty cycle of 1/6 at 25 kHz will likely be fine. 30 V insulation capability pretty much happens by applying any insulation at all. However, the same factor of 6 applied to a 110 V motor would be a bad idea without consulting the manufacturer. 660 V applied to a "110 V" motor could cause damage, even if this is only at the peaks of the PWM and the average is still within specs.