150 volts at outlet?
A typical "Magic 8-Ball" tester like the one you are using will activate with a broad range of voltages. The exact voltage will vary depending on the technology used, but I'd say it is a reasonable bet that anything between 70V and 250V (which would allow for some really messed up wiring without zapping the device or the user) will light up.

The multimeter is a more reliable device when it comes to specifics. It would be very unusual, though not impossible, for a modern multimeter to be 20% off - reading 125V as 150V. As it turns out, the problem was the multimeter battery, but keeping this answer as it could be relevant to others in the future. I would do the following:


Test against a different voltage source. Simplest would be mains voltage in a different building. If that is not an option, try a battery powered device, though AC and DC could be "off" by different amounts. You can also try the output of a device that takes a broad range of inputs and produces one stable output - e.g., a laptop charger will typically take 90V - 250V and output 18V or some other very specific value. Assuming the multimeter checks out OK on other stuff...
Determine whether you have "all high" or "half high, half low". The easiest way to do this is to check a "240V with neutral" receptacle - e.g., for a dryer or oven. You should measure nominally 240V hot-hot and 120V for both hot-neutral measurements. If you get 300V hot-hot and 150V for both hot-neutral measurements then you are "all high" (which I would find very unusual). If you have 240V hot-hot, 150V for one hot-neutral and 90V for the other hot-neutral then you likely have a lost neutral.


If the end result is either "all high" or "lost neutral", CONTACT YOUR ELECTRIC UTILITY IMMEDIATELY. Either one would be a very dangerous situation. "All high" will zap anything that is finely tuned for the standard 110V-120V or 220V-240V ranges. But potentially even worse is a lost neutral - it will zap 1/2 your devices by being too high, 1/2 by being too low ("brownout" type problems) and it can vary unpredictably as devices get turned on and off and pose a real human safety hazard.