"are there any axial modes in a non rectangular room with no parallel surfaces?"
In short (I had no time to type anything):
Walls that aren't parallel do affect modal response, but they don't supress it. That would be nice though. But a good combination of geometry and treatment allows you to "clean up" the room and you can really redirect the energy where you want it to be. The complex modal response of these rooms is such that there is a "constant shift".
All those modes actually combine, whatever the room.