It's a long journey. I looked it up using www.dbahn.de, and here is what I think the fastest connection:
Use OEBB (Austrian railways) Intercity Bus from Venice Tronchetto stop to Villach station, timetable
(if you take the earliest, 09:20, you will arrive at Vienna Meidling station at 17:27, after transferring to a RJ 630 train) 8 hours 7 minutes
the night train departs at 20:02, and arrives in Budapest at 22:49, journey time thus 2 hours 47 minutes
However, your layover time is more than 2 hours at Wien Meidling station
The whole journey can be booked with www.oebb.at
Rumour has it that the daytime trains between Italy and Austria using that route may be reinstated next year.
Meantime there is no rail alternative to the route suggested above.
There are probably flights between the two cities but my internet is too slow to enable me to check that.
Go to a site like skyscanner.net which should give an indication.
There is a direct night train Venice to Vienna leaving Venice just before 9pm. From Vienna you then catch one of the frequent railjet services to Budapest. It's doable, but it's a long journey. We were faced with the same dilemma last year, and ended up breaking this journey with a few days in Vienna.Edited: 19 December 2013, 23:34
Direct train from venice to vienna departs at 4pm and arrive 11.30pm, too late to take a connection to budapest. Might as well break the journey in vienna.
You'll get print-at-home tickets from oebb.at, collect-at-station tickets from italiarail.com.
<or any other way?>
There are indirect flights from Venice, but be very careful of options requiring separate bookings on two low-cost airlines, as a delayed first leg will result in a worthless ticket for the second leg.
There are daily direct cheap flights from Milan. Milan airports are around 3.5 hours from Venice by train - advance purchase tickets for Venice to Milano Centrale start at €9. The train from Milano Centrale to Malpensa Aeroporto costs €10.
For flights, see http://www.skyscanner.net/ but book on the airline's website not on pop-up advertiser agencies.Edited: 20 December 2013, 12:58
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