The word INORY it self is a simple anagram on IRONY.

Inory is the complete opposite of being sarcastic and/or ironic. This word may come in handy for persons that use sarcasm and irony a little bit too often, but that wants to be straightforward, non-ironic, and frank once in a while.

Inory is an oral and verbal marker used in situations where people misinterpret your honest intention of being nice/direct/straight/frank, and misunderstands it as you being sarcastic or ironic.
It is used to tidy up messy situations where sarcasm (and irony) ain’t that appropriate - but where, you somehow, have managed step right into the bear trap of being seen as some kind of insensitive asshole that blatantly flaunts his/her evil wits whenever he get the chance.

In other words: Inory is when you say exactly what you mean, without trying to be smart, witty, hilarious, or bitter.