I recently learned that ohms law is not always obeyed. I found this surprising because I thought ohms were defined in terms of volt and amperes by the equation R=V/I. I did a little googling and found the following definition...

This clarified things a little in that the definition of an ohm specifies exactly 1 ampere, 1 volt, and 1 ohm. So if I have a wire with one ohm of resistance I know that if I apply 1 volt of potential, 1 ampere of current will flow. If however I apply 10 volts more current will flow, the wire will heat up, and its resistance will increase, so less then 10 amperes will flow.

My question is, if other conditions (such as temperature) are artificially kept constant as voltage and current vary, does ohms law hold more true or absolutely true?

Consider a spark plug. If I try to measure its resistance using ohms law while applying 100,000 volts will I get the same answer as if I ionize the air between the electrodes with another heat source and measure the resistance with 1 volt?

What is meant by the statement is that whilst the ratio of voltage to current is always called the resistance (and measured in ohms), this ratio may vary with voltage or current.

So if we plot a graph of current sgainst voltage we may get a straight line of constant slope = ratio of voltage to current. Such a component is called a resistor.

However many components, particularly those based on semiconductors, display a different current v voltage curve.

A particularly stark example is the tunnel diode which has a negative slope at certain parts of its I-V curve.

Resistance is usually meant "for a specific temperature". An ideal resistor has a linear relation voltage<->current, if you keep its temperature and other conditions constant. Many metals are good approximations of ideal resistors (in a reasonable range), even if their resistance depends on the temperature.

May be it will be better to say that non-ohmic behaviour should be thought as variation of current density is not linearly related to electric field applied.