This 'nonsense' being called for is indeed a bit difficult to define, IMO. I don't know whether to write something that is just out-and-out nuts... or whether to write a poem that appears to make sense, but doesn't. (Heck, that sentence doesn't even make much sense, does it? 
I think I know what I was trying to say there.)
Jayne, as you know, the LitRev usually allows a pretty wide interpretation of the subject of the competition, and I imagine that there will be room for all shades of nonsense verse. My own preference is to write something which, like Lewis Carroll, makes perfect sense on its own terms, but where the terms themselves are nonsensical.
'Nonsense' need not be meaningless, e.g. "The Walrus and the Carpenter".