The train has five coaches = The train has five carriages. the former more used now than the latter. The train announcements say 'The front four coaches are going to XXX the rear four coaches are going to YYY' so I'd go for coaches (London are in England).
"Carriage" is used in England to describe a railway wagon for carrying passengers. "Wagon" would be used for carrying freight. "Coach" normally refers to a road vehicle - a bus that is more luxurious, with toilets perhaps, and used for longer journeys.
Does Vagon have any meanings besides railroad car? For example, cou7ld you refer to your automobile as a "Vagon"? It also looks a lot like Wagon.