Are there guaranteed winning strategies for Quarto?
Quarto has been evaluated as draw if both players play optimally. There's a presentation on the result here:

http://www.cs.rhul.ac.uk/~wouter/Talks/quarto.pdf

Quarto seems to have been originally solved by  Luv Goossens in 1998, although I'm not sure whether this was published or not.  The presentation links to this old web page by Goossens:

http://web.archive.org/web/20041012023358/http://ssel.vub.ac.be/Members/LucGoossens/quarto/quartotext.htm