First, if you don't already have them, get some basic electrical test/safety equipment:
- A proximity voltage detector
- A decent multimeter, at a minimum UL listed. You should probably get a category 2 or better.
- A three prong outlet tester that will tell you if a outlet is wired properly/reversed and if it's grounded.
There are circuit testers that you can help you with tracing out the wiring. However, I'm not all that familiar with them. I used a more homebrew approach. I grabbed a small spool of 22 guage bell wire. On one end, I attached alligator clips, on the other I attached ring terminals. This allowed me to hook the alligator clips to a wire I was interested in one outlet box, and then using my multimeter find the other end by checking for electrical conductivity. Just remember to always turn the power off, and VERIFY its off, before testing. I've seen what a 12V short from a lawn mower battery did to small wires. I don't want to think of what 120/240 would do to this test apparatus.
Second, have you made a circuit map of your house? If not, I suggest doing so. Doing so will give you a good idea of what's on each breaker. It will also identify any miswired outlets. Finally, you might be able to discern some of the logic from the previous runs. If at the end of this step it all makes sense, you may also want to consider playing the lottery before you go to sleep.
Once you know what's on each breaker, it'll give you a starting point for actually mapping between boxes. Then comes the tedious part of opening boxes up, and attempting to trace the wires from box to box. As a warning, this will probably take awhile. If you need this done in a reasonable amount of time, you may want to consider a pro. Having the circuit map will also help you identify if the previously owner left live wires sitting in the wall (say when you come across an electrical box with too many wires for the remaining devices on the circuit.
Now for some of your specific questions.
1) Too many wires in a ceiling box:
- Each electrical box has a limit on the number of conductors it can have in it. I suggest you read up on Electrical Box Fill, such as at http://ecmweb.com/nec/code-basics/el..._calculations/
- You're correct that you'll need to install additional boxes to correct the problem. Do you have attic access above the problem box? All of the boxes need to remain accessible. So putting them in the attic will allow you to use larger boxes and not have to worry about how they look in the room below. If you don't have attic access, you'll have to consider if you want to put more ceiling boxes in and cap them off, or if you want to re wire so that the circuit goes from outlet to outlet instead of fanning out from a single box.
2) The furnace light.
- First try turning on every single light in the house. See if it comes on. Second, after you've made the circuit map, see if you can guess which circuit should be feeding the box. Then you can turn off the circuits in the area and see if you can determine which wire goes to the box. Finally, there's the dangerous option. You can use your multi-meter to try and see if you're getting 120 in that box. You may find that you've just got a bad light fixture. On the other hand, you may need to go digging up stream to find what's disconnected. Also, there is a chance that the light was disconnected during one of the other rewirings and never reconnected.
3) The kitchen light.
- Again pretty much the same advice as #2. There are a few options for using xx-3 wire (black, white, red, ground).
a) You're using a switch loop to control the light that's up to 2011 code. Thus the black and white take hot and neutral to the light switch. The red connects the hot to the light when switched on. (seems unlikely)
b) There used to be a ceiling fan located here, so the black/red wires were for switching on the fan and light separately.
c) You're dealing with a multiwire branch circuit. This would be 2 circuits sharing a neutral and being run in the same cable.
d) There used to be a 3 way switch.
e) Someone ran out of 2 conductor cable and finished a run with 3 conductor cable. I would suggest also taking a careful look at the switches in the area. You may find one where the red has been clipped back along with the outer insulation on the cable.
As a suggestion for future posts, I suggest picking one problem and focusing on it. I like you tend to just backup the dumptruck of information and drop everything in the first pass. Often I find that folks tend to get confused processing everything, and on the internet we can't see when folks eyes glaze over.
Also it's much easier to miss small questions in the longer posts.
Finally, welcome to the forums and good luck with this.