cheap transportation from Barcelona to Innsbruck

There is no really cheap way to get between those cities at the last moment! They are almost 1.200 miles apart. You can try last minute flights, as flying is the only realistic option that will get you there in the same day. Else you could try a combination of high-speed trains from Barcelona (Figueres actually) to Paris, Zurich (overnight stay) and Innsbruck, but that will cost 3-digit for sure.

Actually, I found a cheap Ryanair flight from Barcelona to Munich and then a train down to Innsbruck.

Since when did Ryan Air fly to Munich? Last I knew, the closest airport used by Ryan is Memmingenberg Airport , several hours by bus and train west of Munich, closer to Ulm than to Munich. The cheapest, simple connection from Memmingenberg to Innsbruck will involve a bus and two trains via Munich, take six hours, and cost over €60. Alternatively, a somewhat faster, more complicated route would be to take the bus to Memmingen and a train to Kempten, then pick up the Ausserfernbahn through the Tirol (change trains in Reutte) to Garmich-Partenkirchen, then take another train over the mountains via Mittenwald and Seefeld to Innsbruck. For a single person, get a point-point ticket from Memmingen to Innsbruck for €37,20; the bus to Memmingen would be extra.

I can't imagine that a last minute flight on Ryan Air or any budget airline is going to be cheap. However, I can see a $165 flight from Barcelona to Innsbruck for next week on Vayama on www.kayak.com