At the moment, your only option if you want to travel by train direct between Vienna (Wien) and Venice (Venezia), is to travel at night. There are a number of services to choose from however, the majority of which travel between Vienna and Rome, also stopping at Venice Mestre.
This page deals with the sleeper train - EuroNight Allegro service 'Don Giovani', which travels between the two cities also passes through Salzburg and Villach. This is the only train between the two cities that gets right to the heart of the two; Venice and Vienna. The alternative night train option goes to Rome, but only calls at Venice Mestre and Vienna Miedling, whereas this one travels to Vienna Westbahnhof and Venice Santa Lucia. If you don't fancy taking the sleeper train, there are indirect daytime services available, changing at Villach.
The service offers a range of accommodation options, including first and second class sleeping compartments, as well as second class couchettes and seating.