Difference between Incongruous and Ironic

INCONGRUOUS vs IRONIC: ADJECTIVE

Lacking in harmony; incompatible.
Not in agreement, as with principles; inconsistent.
Not in keeping with what is correct, proper, or logical; inappropriate.
Not congruous; reciprocally disagreeing; not capable of harmonizing or readily assimilating; inharmonious; inappropriate; unsuitable; not fitting; inconsistent; improper
Two numbers, which, with respect to a third, are such that their difference can not be divided by it without a remainder, the two numbers being said to be incongruous with respect to the third; as, twenty and twenty-five are incongruous with respect to four.
Lacking in harmony or compatibility or appropriateness
Not similar or congruent; not matching or fitting in.

Characterized by often poignant difference or incongruity between what is expected and what actually is
Humorously sarcastic or mocking
Characterized by or constituting irony.
Given to the use of irony.
Poignantly contrary to what was expected or intended.
Ironical.
Characterized by or constituting (any kind of) irony.
Given to the use of irony; sarcastic.

In the theory of numbers, not congruent: thus, 7 and 8 are incongruous to the modulus 3, giving different remainders when divided by the modulus.
Not congruous; incapable of reciprocally fitting and agreeing; unsuited or unsuitable; inharmonious.
Consisting of inappropriate parts, or of parts not fitly put together; disjointed: as, an incongruous story.
Synonyms Inconsistent, etc. (see incompatible), unsuitable, unsuited, unfit, inappropriate, ill-matched, out of keeping.

Preposterous, Odd, Unlogical, Out or keeping, Discrepant, Inconsistent, Unreasonable, Inappropriate, Unfitting, Incompatible, Ironical, Illogical, Inharmonious, Ironic, Absurd

Puzzling, Odd, Ludicrous, Strange, Funny, Absurd, Paradoxical, Surprising, Ironically, Dry, Wry, Humourous, Humorous, Incongruous, Ironical

Preposterous, Odd, Unlogical, Out or keeping, Discrepant, Inconsistent, Unreasonable, Inappropriate, Unfitting, Incompatible, Ironical, Illogical, Inharmonious, Ironic, Absurd

Puzzling, Odd, Ludicrous, Strange, Funny, Absurd, Paradoxical, Surprising, Ironically, Dry, Wry, Humourous, Humorous, Incongruous, Ironical

Ironic, yes, but all too likely given tyesteryear.
His tactic, nevertheless ironic, also complimented our humanity.
In an ironic sense Karl Marx was right.
Heroic: The Ironic Self in a Hyperbolic World.
But there was to be an ironic twist.
The whole situation is just a bit ironic.
His work is often ironic, erotic or comic.
In line with this consideration, intelligence may be more relevant for the detection of ironic praise than for the detection of ironic criticism.
You could hear the seeds of something and ironic enjoyment that in the years to come would stop being ironic.
Is the Detection of Ironic Criticism and Ironic Praise Associated with Abilities and Traits?