Irony, reflection, and dialectic are all practices that let us become aware of other possibilities. They can be rhetorical — methods of speech — or methods of thinking, since thought is much like self-talk.
Start with irony. If we respond to a judgment with an ironic “yeah, right!” we are pointing out that one could judge differently. If the parent says “Now that you’ve graduated from college you will get a job and be happy.” the adolescent’s response “Yeah, right!” suggests other possibilities — that she won’t get a job, or won’t become happy, or that she might instead die in an automobile accident.
Pointing out possibilities can be bitter and critical but need not be. It could be joyous. If we have no money for Christmas and you say “Christmas is cancelled this year.” I can respond “It sure is” ironically, because I think there is another possibility — Christmas is not cancelled because, like the hoos in hoo-town we can have a great Christmas without presents, or because I have a lottery ticket in my pocket I haven’t told you about yet. However, irony is often used in the service of critique because to suggest other possibilities suggests that the current arrangements might be bad, or at least sub-optimal.
Irony is part of a group of practices that make us aware of other possibilities. Dialectic is another one — the practice of asking “why do you think that?”. Reflection is a third one — the practice of taking our judgments or speech as itself a topic of judgment of speech (the metaphor is looking at the judgment and speech in a mirror).
These practices have twins that try to make us not talk about other possibilities that we all kind of know are there. Sentimentality, hypocrisy, and bullshit are such practices but there are many of them. Unlike the possibility-pointing practices which try to make us aware these try to make us less aware (or pretend to be less aware) so they can be less explicit and conscious. So simple self-distraction and changing the subject, as well as various forms of splitting and histrionic self-dramatization are part of the complicated modern human being’s tool kit. People sometimes talk like the ironists are having a field day and the people who just want to get a job and have a family are cowering before them, but this is false; the powers of the anti-ironic (ant anti-dialectic and anti-reflective) practices are, generally, much stronger.
If it is impossible for us to become aware of another possibility — e.g. we are dying of thirst and confronted with water — irony and its related possibility-suggesting practices has no toe-hold with us.
It is possible to be ironic about irony. So, suppose we are confronted with a person who is using irony mechanically. Without even listening to what we say this reflexive ironist responds “Yeah, right.” We can say “It’s great how you are using your ability to point out possibilities” meaning there are other options than pointing out possibilities — in other words there are other possibilities than irony.
The higher order version of irony is irony about irony, about reflection, double reflection, about dialectic, just dialectic, since the possibility of talking about talking is baked into that notion. These phrases I believe work for any sort of n+1 version of the practice. In other words, I am pretty sure there is no important difference between being ironic about the possibility of irony, and being ironic about the possibility of being ironic about the possibility of irony. But if I am wrong please let me know in the comments.