...all the other duplexes in the home are fine and read 120V. There's one though that has wierd readings - 18V, 19V, 20V, etc.
What would cause something like that?
Digital True RMS tester is all I use. I will never use a wiggy style tester again. If you learn how to use the tester properly it will be a invaluable tool.
Those wiggy testers may have been useful at one point in time, but today you have capacitors, resistors, inverters, inductors and all kinds of other funky stuff causing of electrical distortions on the line. While this maybe a headache for some who don't like reading all the extra garbage and trying to understand it, I've found it to be helpful in troubleshooting electrical problems. Especially in the so called "smarthomes" that use a butt load of capacitors and inductors for home automation.
But to answer your question, I'd like to think you have all the receptacles pigtailed. If you are testing a receptacle on the branch circuit and it should be reading 120v line to neutral, but instead you are reading something other as 30v or 15v or other, there could be a few possible causes.
One that comes to mind is a switched outlet. If the switch is off, the digital tester will pick up residual voltages floating around on the neutral causing inductance which registers impedance(Z) and wallah you have voltage.
A bad pigtail could cause readings like that.
You could help by providing more details. Letting us know the voltages from neutral to ground, neutral to hot, hot to ground and so on. You could also tell us if the receptacle is a dedicated circuit or a branch circuit. What type of wire was used, ie romex, mc, .... What else is turned on while you test. What is off.
While it may seem a little overkill, these are things you will have to consider when troubleshooting circuits.