"Venice to Klagenfurt and Vienna by Train" By train (Santa Lucia station) Tip by lotharscheer

There is only 1 direct train from Venice Mestre, leaving 1.30 am to Klagenfurt arriving 4.40 am, and on to Vienna arriving 8.34 am and 1 1rain from Venice St. Lucia at 9.05 pm via Salzburg arring at Vienna at (8.22 pm), this you can book online on the OeBB site
http://www.oebb.at/en/index.jsp
from € 19 to Klagenfurt and € 29 to Vienna, but in the train you you have to find first the austrian conductor in the sleeping car to validate your ticket (or validate it if you are earlier in Austria at a OeBB train station). It is € 69 to Vienna if you book with Trenitalia.
OeBB has also several daytime buses leaving from Venice Tronchetto, last stop of People Mover (the bus stops also in Venice Mestre), from € 19 online, no problem of Validation there.
If you want to go by train in the daytime there is a new regional train company from Udine (leaving 7 am and 5.15 pm, 2 hours) to Villach (leaving at 9.40 am and 7.9 pm for Udine), no need to book for the connecting train to Udine but from Villach it will be cheaper if you book online (from € 19).

Mode: TO
Type: Train