I can see why you asked a question on this. What makes this question so hard is that it is vague, and therefore could either be irony or paradox.
We can automatically rule out hyperbole and allegory; hyperbole is overexaggerating things, for instance, "my backpack weighs a ton!", and allegory is used to describe something that has a deeper meaning, usually moral or political. A good example of an allegory is Dante's Inferno.
So the real question here is, "is this referring to irony or paradox?" And the information itself doesn't really pose an immediate to that question; both irony and paradox could fit the categorization 'surprising, interesting, or amusing contradictions'.
If I were you, I would go with paradox. To me, paradox is more interesting than irony. Paradox is very similar to oxymoron. For instance, if someone said, "deep down, you're really shallow", the reader would likely read it and go "hmm...", maybe having to double-take to truly understand its meaning. Whereas, with irony, it's kind of more predictable; for instance, when you're reading a story and someone comes up with a very foolish idea and one character says, "Oh, what a great idea!" you can pretty much tell that they were using verbal irony, and it's not as amusing. But paradox comes out of the blue when you're least expecting it and you're often like "what?" and have to reread to understand it.
If the correct answer does turn out to be irony, I'm really sorry. But hey, it was a pretty subjective question! I went back and forth between the two for a while!
Hope my explanation helped at least a little bit.
