The Hudson never had true overnight commuter service, although until around 1959 both Hudson Div. suburban timetables and NYC system timetables show a local train to Syracuse departing GCT around 3AM that made many, but not all, local stops in the suburban territory on the Hudson. That's all for the Hudson.
The Harlem had the "Night Owl" service starting in either late 1966 or early 1967. In the beginning it consisted of hourly departures (2AM to 5 AM) out of GCT to North White Plains stopping at Fordham, Mt. Vernon West and all stops from there to NWP. There were departures out of NWP to GCT at 3AM and 4 AM. Not long into the service the 4AM train to NWP became weekends only, but it remained this way into 1972. The July 17, 1972 timetable shows GCT-NWP service reduced to 3AM and 4:30AM departures from GCT, and the NWP-GCT service reduced to a single 3:27AM train out of NWP. These remaining trains were eliminated one year later in July 1973 when GCT was closed for the first time ever between 1:30AM and 5:30AM.
The New Haven a couple of trains through the years that departed GCT around 3AM and 4:30 AM making local stops to Stamford with either one or both of them continuing on to New Haven. I'm not sure about the details of these trains in the New Haven RR days, but as of the April 26, 1971 timetable there was a 3:10AM Stamford local and a 4:40AM local to New Haven. By the July 17, 1972 timetable the 3:10AM Stamford local was gone, but the 4:40AM to New Haven was still running. That train was eliminated in July 1973.