I just woke up to find the pressure valve on our water heater shooting out cold water ( not hot - it may have flooded out the natural gas burner at the bottom ) and flooding the house. ( someone removed the vertical pipe from the bottom of it, if it had one, so it was flooding outside of the bottom drain pan ) It may have been doing this for 90 minutes since I got up before to use the bathroom - the last time I was up and it wasn't doing it. I shut the water off and called the water company and they say it's not overpressure from them. ( though the pressure here sometimes goes to 90 PSI normally )
Assuming that you in some way verified that the pressure was no longer over 150 psi, the T&P relief valve should have closed. Since it didn't, replace it. Shouldn't be a difficult install other than putting a new drain line on it. (Note, do not reduce the drain line size. Relief devices should never have a smaller outlet pipe size than the size of their discharge.)
Jim is right, get a peak pressure guage. There is a very high probability that if you do not have a thermal expansion tank, the water heater relief valve is going to hit 150 psi and leak a trickle after shower/bath cycles of the water heater. And without a PRV on the water supply line any impulse to the line could pop a relief valve open as well.
Before I replaced the toilets in our house the water heater relief valve had no issues. Turns out the old toilets were acting as relief valves trickling a little pressure off at about 120-125 psig when the water heater cycled. When I put in the final new toilet, this source of relief was gone and I started getting puddles at the T&P drain. I confirmed the problem with a peak pressure gauge. So I had a thermal expansion tank installed.
This might not have been an issue many times in the past, but with utilities now preventing back flow at the meter, and with various appliances having better shut offs, there are fewer sources of relief for thermal expansion.
We do have a problem when the whole house humidifier runs sometimes. It can take a trickle of hot water from the water heater and cause the temp to go up quite a bit, but it hasn't caused the pressure valve to go off like this.
I'm not following this. A trickle of hot water to the humidifier shouldn't be causing the water heater temperature to vary greatly. The thermostat on the water heater should kick in when the temp falls a few degrees (I'm not sure how much offset it allows before it is triggered.) If the temperature is spiking from this then I suspect there is some other issue with the water heater. You said in a follow up post that you are running the temp at maximum, why? Is there something about the usage/size of the water heater that is requiring this?
If you are doing deep cycles with the water heater temp set to max, then the thermal expansion issue will be a bigger one than for someone running a lower water heater temp.
What's the likely cause of this? Do I need a plumber or should I just try and replace the valve myself?
See the above and Jim's comments. I suspect you are going to want a plumber because there will be other important work to do to eliminate the root cause. The key is to locate a plumber that is a good troubleshooter and can work out the sequence of events that caused the problem. I wouldn't want to just slap a band aid on this...