Rail services of the Austrian national federal railway company OEBB have seriously deteriorated the last few years. There are no direct connections to France, Belgium, Netherlands any more and the rest is a fragment. On domestic connections passengers suffer from delays, overcrowded trains, bad service and all sorts of unpleasant experiences including overcrowded trains cleared by the police.
Most important for tourists with bicycles is that in 2010 most of the trains that still had bicycle capacities were robbed of the luggage van.
Few of them are left: Ljubljana (Slovenia), Hamburg (Germany), Zuerich (Switzerland), Praha (Czech Republic) and Bratislava (Slovakia).
Some connections do not exist even without bike transportation. For example there is not one train that goes directly between Graz and Linz, the second and third largest cities of Austria.
All trains indicated as "Oebb EC" and "Oebb IC" are usually run without an adequate service for bicycle transportation. Yes, almost all transport them according to timetables. But!: You have to do it the following way. First you have to find the one railway carriage where the place is. Then you have two options, because on each of the two entrances of this one carriage you have a bicycle symbol, but only one of the two is the right entrance and you cannot see from outside which is the right one. But you have a compulsory reservation. so you have to find it out. Then you to climb in three steps with the bicycle and all. After this, turn around 90 degrees and shove everything through a narrow passage, nearly as narrow as your handle-bar. Hopefully there is no one to step out of the toilet at this moment. The door is not really a grave problem for a dedicated activist and alas finally you are in. Half done! Now you stand on a small place just behind the seats, you turn to the side and see a hook. The free place under it is as large a seat. So one way or the other you have to turn around 180 degrees and hang you bicycle on the hook. There is one such place for only one person on each end of the carriage. The lonely fighter is the right passenger for this kind of "service". Even couples are too much of a crowd, not to mention whole families or groups of friends. Now, imagine that those trains are generally overcrowded, you have some luggage with you and you enter or leave in a station where lots of people move in and out through the narrow door and the train stops only for three or four minutes.
In practice this kind of operation mode was invented not to provide a possibility for passengers, but to get rid of them.
There are few options left. Use local (S-Bahn), regional (R) or regional express (REX) trains whenever possible. No reservations required, enough space and all you need is time. With these trains you can usually reach the border of the federal county (Bundesland) where you are in. For example you can go from Wien (Vienna) to St. Valentin (Lower Austria) near Linz.
Do not rely on national trains. There is some chance that you are stranded, especially if you have to travel from or to Wien (Vienna), the east of Austria (Niederoesterreich, Oberoesterreich, Burgenland) and the south (Steiermark, Kaernten). The situation in the west is somewhat better because there you have access to trains from the German railways (DB). If you are in Vorarlberg always go to Switzerland to continue an international journey.
If you are finally in Wien, for example because you followed the Danube, you may find adequate train services from Bratislava (Slovakia) and Breclav (Czech Republic). Both have good access to international rail traffic and the Slovakian and Czech railway companies still know how to provide a minimum of "comfort" like a luggage van. From Vienna there are very good connections (about one hour travel time) to those destinations. Buy a cheap "Euregio ticket" which includes the bike transport fee. No reservations needed for these trains and there is enough space for your bicycles. All other tickets (international and domestic) buy in Slovakia or in the Czech Republic, because it is much cheaper there.
The two day trains that had always enough capacities even in peak periods are now "Railjet" trains and so "fast", that bicycles are not allowed. So there is now one night train instead, and the place for about ten bicycles is insufficient during the summer. So the places are booked weeks in advance. The bicycles hang on hooks with free access to everyone any time all night. If there is not a peak time Oebb just does not send this carriage to Zuerich. so you have a reservation and payed for the transport but no space. Finally the conductor tells you to squeeze your bike into a compartment and put it on the seats. Do I have to say that normally it is strictly forbidden to take your bicycle into a compartment and you have to pay a penalty if you put your dirty bicycle on a seat?
Still pure bureaucracy. You have to order a lorry 14 days in advance (!) to pick your luggage up. It needs 4 or 5 work days to arrive at the destination. In Switzerland this may be a railway station, in Germany it must be a home address. For no other countries available.
Plan carefully or you may get into a situation where you do not know how to get home with your bicycle.
If you want to have good train services, go elsewhere. In the Czech Republic and in Switzerland you have excellent connections and a reliable service. You can store your bicycle at railway stations as left luggage, send it to other destinations easily or take it with you in most of the trains. None of this is possible in Austria.