Across 25th in Bellwood may have actually been CGW track, as I have a 1975 system timetable map showing an isolated stub between Maywood and Bellwood. Unfortunately, there's no reference to it in the timetable itself.
The C&NW route was originally built as the Galena and Chicago Union RR--Chicago's first--and went west to West Chicago before heading up towards Elgin and eventually Freeport. It never made it to Galena. When the transcontinental railroad was under construction in the 1860's, a race ensued between C&NW, CRI&P, CB&Q (I think), and possibly others, to be the first railroad to reach Omaha, NE. Prior to that, all materials for the UP were brought up to Omaha by river. At this point, the North Western started building west from West Chicago and relegated the Rockford/Freeport line to branchline status--for those who never knew, C&NW won that race.
The eastern end of this orignal route terminated on the other side of the Chicago River, eventually reaching Navy Pier. What's left of it is pretty well documented at www.chicagoswiching.com
The CGW line was an extension of a route graded for the St. Charles Air Line RR, which included construction of the Fox River bridge in St. Charles and the drawbridge over the Chicago river used by C&NW and BN to reach the IC. Most of the StCAL was never built, but eventually what had been graded was used by the then-abuilding CGW. Right around Villa Park, this line went over the C&NW main on a bridge. East of Byron, a fair amount of this CGW line was retained by North Western into the 70's to serve local freight traffic, but it only ever had CGW passenger trains.
Largely, the CA&E tended to parallel the CGW ROW through the near western suburbs, and the CGW proper crossed both the EJ&E and C&NW Freeport line just north of West Chicago. This W. Chicago-Villa Park segment survived into the 80's and early 90's to serve such customers as Ovaltine, a Smurfit-Stone box factory (until about '93), and now exists as a short spur to a fence manufacturer.
That I remember, I've never run across your original reference to the Geneva line as CGW, but who knows what they meant by it?