Digital multimeter is reading erratic resistance ohm values

In short, yes.

The way a digital multimeter measures current (not a loop current meter) is that it measures the voltage drop across a small precision resistor. For reliability, simplicity, and repeatability, no switches or contacts are placed in series with this shunt resistor. Some meters will have a fast-acting fuse to protect the shunt resistor. Basically, the switches will control the electronics hooked up to the shunt resistor, but they won't disconnect it.

You can perform an experiment with your meter as some degree of proof that this is true. If you configure your meter to read resistance, put the positive probe into the positive current probe socket. You should measure a very small resistance. This shows that the meter doesn't disconnect the shunt resistor while in a separate mode. It would be a small leap of logic to say that if it didn't switch off the shunt resistor then, it probably couldn't when the meter is off.

Alternatively, you could measure the current using a second meter.

Based on your voltage measurement, it looks like your resistor is about 38 ohms, not 332,000 ohms. The current limit on your ExTech multimeter is 200 mA according to the datasheet. The meter is showing about 60% over that limit. My guess is that you either partially blew a fuse or triggered some internal current limiting circuit, so most of the voltage is being dropped across the current meter. Alternately, if the resistor actually was 336k, it might have burned out and failed short after dissipating 0.75W. You'd probably have noticed a smell if that were the case, though.