I was 17 when the ex L&Y Spen Valley line from Low Moor to Mirfield lost its passenger services on June 14th, 1965.
I remember a roughly hourly passenger service from Bradford Exchange to Huddersfield, with some trains extended to Penistone, operated by 2-Car Metro-Cammel [later Cl.101] dmus. They never seemed to be exactly over-crowded.
Occasionally, Leeds Central/Bradford-London King's Cross services were diverted that way to Wakefield Kirkgate and Doncaster, when the main line through Wakefield Westgate was closed.
I believe freight at that time was simply the local pick-up goods.
When the line was closed to passenger services, the section from Low Moor to Thornhill was retained for freight traffic, and a new spur was built from Heckmondwike to link into the ex LNWR route to serve an oil terminal at Liversedge.
I don't remember this being too successful, as the stretch from Liversedge to Thornhill was closed completely in the early 1980s.
I think the line from Heckmondwike north to Low Moor was aquired by the West Yorkshire Transport Museum project which was based at a new site in Low Moor, but that in itself went into liquidation only a short time after opening.
Regarding the stations, Cleckheaton Central received notoriety, in that in 1971 it was reported as "stolen" - the only station on BR to have been stolen!!
Full report here:-
http://sparkonline.blogspot.co.uk/2011/12/mystery-of-stolen-station.html