RDK, Based on what you have told us thus far, Here is what I suggest. First, fix what has burned up and disconnect the light circuit(s) in questioned. Varify that power and system is kosher. The burnt equipment could be the source of the problem.
Once that is all done. Varify you have the proper voltage on each leg going out to the lights.
Then ask yourself, "If I was going to run the conduits for the lights, how will I do it?" This can give you a starting point where to start looking. Once you can confirm conduits and wire routing, document it as an as-built. Check the connections. At each piece of equipment, check to see each light is rated for the voltage and that you have the correct voltage at each light. Document your findings.
I suggest if you feel comfortable doing this is if possible, locate a junction in the wiring that is in the middle of the circuit. De-energize the circuit(s), properly open the circuit(s) after properly marking them and protect all exposed ends. Energize the circuits. This will tell you several things. Whatever is energized and de-energized will tell you what side of the opening in the circuit(s) each load is on. If the goofy voltage dissappears, the problem is on the de-energized portion of the lighting system. If the voltage is still goofy, the problem is on the energized portion. Keep on repeating this until the problem is found. It may not be easy but highly effective. The theory here is you can have a ciruit with 1 million good splices and 1 bad splice. You can find that bad splice within 20 guesses by using this process. Keep in the back of your mind that there can be multiple problems and they can be on both sides in the open circuit so do not get tunnel vision. Also do not let burnt out bulbs trip you up.
When tracing circuits and conduits, do not be suprised to come to a relization that there is a junction some where like a hand box or junction box that you are not aware of. Keep us posted. I like these type of problematic issues. I know, I'm a sick individual.