The wiring in my house is... odd. Nearly every pair of outlets has one of the outlets connected to a light switch. Sometimes that switch is quite far from the outlet even when there are other closer switches that seem to control nothing at all. Sometimes that switch also controls overhead lighting, which makes no sense to me from a design standpoint. Sometimes that switch is a dimmer switch, which is a really horrible idea as if you plug anything other than a light bulb into it, like some electronics, the dimmer switch could do them a lot of damage. One such dimmer switch is also connected to a ceiling fan, and setting the switch to anything less than full does not change the speed of the fan, it just makes it a lot noisier (AC induction motor, obviously).
There are light fixtures that don't seem to have any power to them and aren't controlled by any switch, though I could believe the switch might just be hiding somewhere. There are also switches that seem to control absolutely nothing, though I could believe I just haven't found what they're connected to.
The oddest thing I have found though has to do with the circuit breakers around overhead lighting. I have a chandelier in my dining room that is connected to a dimmer switch. When I moved in, all of the bulbs were incandescents, and I wanted to be more energy efficient, so I replaced them all with dimmable LED bulbs. Now however, I could not turn the chandelier fully off, with the dimmer switch all the way down, the lights still dimly shone. This had never been an issue before, but I thought it probably meant the dimmer switch was faulty, and it was just the different voltage response curves of the incandescents versus the LEDs that meant it had never been noticed before, so I set out to replace the switch.
Now there are two circuit breakers that are relevant to this chandelier. One is labeled "dining room," the other is labeled "lights." As far as I can tell, the dining room breaker controls all of the outlets in the dining room area, while the lights breaker controls all of the overhead lighting in the house.
Here's where the odd part comes in. If I turn off the dining room breaker, the lights stay lit. I have turn off the lights breaker to switch off the lights. However, if I only turn off the lights breaker, and go into the switch panel with my voltmeter, I am still detecting 100V AC across the switch (with it off), even though the lights stay off when I turn the switch on. In order to remove the power I was detecting, I have to also turn off the dining room breaker, even though the lights were staying on when I switched that off.
This conforms to no type of electrical theory with which I am familiar, though there might be some peculiarity of household wiring I don't know about that explains this. Can anyone tell me what might be going on?
Update 3/24/19: After replacing the dining room dimmer switch with one specifically designed for LEDs, those lights are now working quite well. Based on several people's advice in this question, I have now set out to replace the bedroom dimmer switches that are connected to outlets with toggle switches. Have run into additional issues detailed here.