Perhaps addressing the differences between the processes of implication and inference might be helpful.
An implication is a statement (or a whole bunch of statements combined) which suggests indirectly (or implies) a meaning which, for whatever reason, might not be appropriate, tasteful, or polite if stated baldly or bluntly.
A waiter in a hurry to clear your table for the next customer might imply his desire for you to leave posthaste by saying, "And how was your meal, sir (or ma'am)," with an emphasis on was..
If you are sufficiently astute, you will make a correct inference--an inference being by definition a possible, though not necessarily accurate, interpretation of an implication. In this instance your inference might be "Oh, the waiter wants me to leave." By the same token, however, if you lack sufficient astuteness, or the waiter is much too indirect (such that even a member of Mensa would not catch on to the waiter's implication), his implication failed and you made no inference whatsoever.
Indirect speech can be described in various ways and through a variety of words, such as:
- oblique communication
- evasive communication
- communication by innuendo
- a sidelong comment
- circuitous phrasing
- a roundabout way of getting to the desired point
- periphrastic verbiage
- a surreptitious technique (which implies a certain shadiness, which is not present in a waiter's hint, unless the waiter happens to hate you for being a lousy tipper, and a great tipper is waiting impatiently for a table--your table)
- an insinuating comment (which is usually derogatory by nature)
- ambiguous statements, which can be interpreted in at least two--and sometimes divergent--ways, such as when the waiter says "Are you finished with your dinner, sir?" and the diner assumes the waiter means "Are you ready for dessert?"
In conclusion, irony is perhaps the most complicated and potentially dangerous form of indirection, particularly when the ironist's league of potential co-conspirators are not sufficiently astute to infer that a spoken or written statement is in fact ironic.
Randy Newman (songwriter, movie soundtrack composer, conductor, pianist, and all-around wise guy) tends to use irony in many of his songs. Years ago he faced a good deal of opposition when his song "Short People" was played on some radio stations. That was in 1977. Forty-two years later, there are still people who are offended by the irony in Newman's song.