The Orient Express stopped running in 2009 (after it had already been successively cut back to just Strasbourg-Vienna), although it was a "normal train" in most senses (it was a regular EuroNight service, not really any different to ride from less famous ones like the Cassiopeia or Jan Kiepura).
The train you may be thinking of, a luxury train that imitates a historic one, is mimicing the the Simplon Orient Express which did not run through Vienna (and also it rarely goes beyond Venice).
I was in fact thinking of the luxury version. I was not aware it was an imitation.
It's been indeed renovated, and it does London -> Venice and London -> Istanbul, but is outrageously priced (20k eur for Paris -> Istanbul if I remember)
I did the same "route" but took some random night trains between each city, which is much more affordable