Saying a resistor is ohmic and a diode is not is fine by me, but yet a diode still obeys ohms law, only the parameters for satisfying ohms law requires a bit more information. In the end the vdrop of the diode and current through the diode at a given time will still obey ohms law and give R.
No, a diode does not obey Ohm's law. Ohm's law is a property of a material, specifically resistive linearity with respect to current. Since its voltage vs. current plot is not linear, it is not ohmic with respect to Ohm's law. A diode and everything else does have a resistance or impedance defined by V=IR or V=IZ at all currents and voltages that do not destroy it. Again, V=IR is not Ohm's law, is is the definition of resistance or impedance.
With respect to 'ohmic', depending on the context, it means whether something follows Ohm's law (resistive linearity) or whether something has a resistance like a switch contact. I believe these two contextual meanings cause confusion.