I think only the system's creator can give a canonical answer. Speaking personally...
In the spirit of roleplaying in general, and of such a wild and open game as Genius, I'd say "hell yeah!" Almost anything a player can describe should be possible, if his or her character has the necessary axioms. Granted, the PDF (I'm referencing the 1.1 version) is ambiguous, suggesting at one point that the axioms are general, and in another that they are indeed limits:
Page 66: Each Axiom covers a general effect or approach [example].
Page 136: To design a wonder, the genius simply selects one that he can build, based on the limits of his Axioms.
Still, Genius is essentially an evolution of Mage, which definitely does encourage players to come up with their own magic. So even without an explicit rule, I'd absolutely allow creative wonders.
Of course, the axioms are quite broad:
Page 156: The Axiom of Apokalypsi is used to build communicators, scanners, and analyzers. Anything that transmits information to or from the genius is the province of this subtle but powerful Axiom.
That covers a lot of ground, and it's just one of eight. Please do give examples, I am quite curious to know what crazy things your group came up with that don't seem to fit any of these!
