Difference between Incongruous and Ironical

INCONGRUOUS vs IRONICAL: 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
Pertaining to irony; containing, expressing, or characterized by, irony.
Addicted to the use of irony; given to irony.
Characterized by or constituting (any kind of) irony.
Given to the use of irony; sarcastic.
Feigning ignorance; simulating lack of instruction or knowledge; exhibiting Socratic irony.

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.

Addicted to irony; using disguised sarcasm: as, an ironical speaker.
Hence Conveying or consisting of covert sarcasm; sarcastic under a serious or friendly pretense: as, an ironical compliment.
Pretending ignorance; simulating lack of instruction of knowledge. See irony, 1.

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

Laughable, Poignant, Absurd, Funny, Comical, Paradoxical, Satirical, Moronic, Sarcastic, Dry, Wry, Humorous, Humourous, Incongruous, Ironic

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

Laughable, Poignant, Absurd, Funny, Comical, Paradoxical, Satirical, Moronic, Sarcastic, Dry, Wry, Humorous, Humourous, Incongruous, Ironic

It is ironical that whatever SRK does, Ak does better.
Though his words are ironical, they probably indicate that Catholics already applied it to the pope.
Mobile is it sounds ironical if you want a regular communication requirements, the user of free.
His softly ironical yet affectionate treatment of feminine ways is especially admirable.
What could be more ironical than the fact that a disquali.
This ironical exclamation is very common in our old dramatists.
Even his spectacles seemed to wear an ironical gleam.
The gamin of Paris is respectful, ironical, and insolent.
The lead cases came in an ironical order.
His language is pithy, critical and often ironical.