Venice is actually quite easy by train.
Eurostar to Brussels.
Belgian IC to Welkenraedt
cycle 11km to Aachen Hauptbahnhof
regional train to Cologne
Austrian nighttrain from Cologne to Munich (or Innsbruck)
Austrian daytrain from Munich (or Innsbruck) to Venice.
I would prefer this option.
You can actually do a slightly better version that doesn't require the 11km ride to Aachen.
Take the Eurostar direct to Amsterdam, then from Amsterdam you have a choice of either a train to Arnhem, then the regional train to Dusseldorf for the train to Munich,
Or you can take the Berlin train, and change at Osnabruck, then on to Köln, and follow Ivo's route.
Hmm, thinking about it further. There is one slow train a day from Brussels direct to Basel via Luxembourg. So Eurostar to Brussels, then Brussels to Basel, then Basel to Innsbruck, Innsbruck to Venice. It may work better on timing to get the train from Basel to Zurich, then Zurich to Innsbruck. If you're in no rush, and want to enjoy your journey as much as your destination, between Zurich and Innsbruck get off at "Buchs" and cycle across the border to Liechtenstein. Have a coffee in the Capital Vaduz, then take the fantastic climb into the centre of the country via Steg to Malbune. Have lunch there, then descend back down to Buchs, to continue your journey. Liechtenstein is a fantastic place to visit. It's like a bitesize Switzerland. Does nice wine, which they don't seem to export. (Useless trivia, worlds largest exporter of false teeth...)
Long distance EU trains that accept bikes are not as common as they were, the High speed trains don't like you taking a bike. But there are a few trains each day that do accept bikes. (IC8/9 Hamburg<->Zurich for example). The Bahn.de planner has a useful "bike space required" option, that will only give you routes that accept bikes. Tho it can get a bit confused by some Benelux combos due to NS putting incorrect info in their system. (Officially you can carry a bike on the Brussels<->Amsterdam Slow train, but in the system it's marked as only between Brussels<->Essen, and Rosendaal<->Amsterdam, which confuses the planner).
This is my primary reason for my new bike being an S&S coupled bike. Means I can box it up and get on an ICE train, makes travel a lot easier.
J