What are some examples of irony in Anton Chekhov's The Bear?

Irony is a literary technique where a statement is used to communicate the opposite of its meaning usually for emphatic or humorous effect. The term also refers to situations where results or conclusions are intentionally made to deviate from the typical expectation for a humorous effect.

Smirnov mocks Popova’s “state of mind” which does not allow her to discharge her family’s financial matters. He ironically responds to Popova by stating that he is also in a “state of mind” because of the debt he is in, and he needs to be paid immediately.

SMIRNOV. Well, there! "A state of mind."... "Husband died seven months ago!" Must I pay the interest, or mustn't I? I ask you: Must I pay, or must I not?

Smirnov further mocks Popova by asking her if he should escape from his creditors in a balloon or knock his head against a brick wall.

Do you think I can fly away from my creditors in a balloon, or what? Or do you expect me to go and run my head into a brick wall?

Smirnov states that he dislikes talking to women, and he’d rather sit on a barrel of gunpowder.

That's why I never did like, and don't like now, to have to talk to women. I'd rather sit on a barrel of gunpowder than talk to a woman.

Smirnov also suggests that he looks well. However, his description is contrary to his actual state.

I must say I look well! Dust all over, boots dirty, unwashed, unkempt, straw on my waistcoat....

He further mocks Popova by speaking to her in French and telling her that he is happy that she has not paid the money owed.

How do you want me to talk to you? In French, or what? [Loses his temper and lisps] Madame, je vous prie.... How happy I am that you don't pay me.... Ah, pardon. I have disturbed you! Such lovely weather to-day! And how well you look in mourning! [Bows.]

Anton also builds the irony throughout the play because it is unexpected that after a highly heated exchange, Smirnov and Popova would fall in love instead of proceeding to the gun duel.

The kiss at the end of the play contradicts all the negative statements made by Smirnov and Popova. In addition, the ration of oats for Toby is completely withdrawn for the day because Popova has fallen in love with Smirnov.

POPOVA. [Lowering her eyes] Luka, tell them in the stables that Toby isn't to have any oats at all to-day.