Strasbourg to Budapest is 663 miles (~1060ish Km) according to one of the online maps. As this used highways to calculate, figure adding at least another 30-40%, so somewhere of a total of 1500Km.
1500Km/80Km per day= 19 riding days. 3 weeks seems a good general guide from your door to Budapest, with a rest day every 7, and ample time to check out "touristy" bits along the way (historical sites, etc).
-Camping-
Free camping seemed generally frowned upon in Austria along the Danube, yet there were some hardened sites as I recall-but few and far between. Shouldn't prove a problem to an experienced leave no trace free-camper though. The pay campings were 8-15Euro 6 years ago, and easy enough to find.
Free camping was much easier in Slovakia & Hungary, the pay campings were much better value at that time too. For a real treat you can even include a few nights in a Pension' in Slovakia/Hungary-price realy depends upon time of tourist season.
-guides-
Check out cycotourers suggestion above. Finding guidebooks along the way in english for the route beyond Vienna proved impossible on 2 occassions. Can be found in German with relative searching at better map shops ie Freitag&Berndt Vienna.
-Suggestion-
If the weather is good, stay on the Slovakia side as long as possible. I really enjoyed the open riding along the river wall (?dike). Since you are exposed all day long, it would be awfull riding in my opinion if foul weather (head wind, rain etc). In the event of foul weather, cross into Hungary early and follow a road route.