How can I objectively measure train noise from a sound recording?
One of the radio stations around here used to have the slogan &quot;It may not be your favorite song, but it has a lot of the same notes.&quot;  A DFT analysis can tell you what notes are present, and at what intensity.  With calibration, you can even measure the real world level.  This doesn't get anywhere near psycho-acoustics though.
What you could possibly use it for it to define an objective measureable standard of when the greasing needs to be done.  The loudness of the noise is going to be dependent upon where you measure it, so calibration and absolute values aren't that useful.  What you need, as you alluded to, is comparable recordings of the sound when the tracks are well greased vs when they get annoying.
With those in hand there are several techniques you can use to make quantitative comparisons.  The difficulty for you is that your intended audience will likely not have the technical understanding to comprehend any sophisiticated analysis so you are going to have to try to reduce down to a simple number or two, or a nice visual image that expresses the data succinctly.  I think you already have the latter with your spectogram.  For the former, a simple sum of the magnitudes of the bins in the frequency range of interest should be adequate.
Now, if you can track such a metric throughout a greasing cycle or two, then you can establish objective criteria (by association) of when the noise has reached the same level of annoyance.  Just because you are a concerned citizen, maybe you could email this value to the railroad company for every train passing and they will gladly monitor your numbers, thank you for your service, and send somebody out every time it reaches a threshold value.
Dream on?  Yep.
If there is a local noise ordinance, you can perhaps work with your local politicians  rather than the transport authority.