In Part 1, Chapter 7, the narrator uses both a simile and a metaphor ironically, using a combination of three figurative devices to create a single sentence. Here, he discusses the idea that man has become kinder over time because of the evolution of civilization, although it is clearly untrue, as evidenced by the sheer amount of wars going on around the world:
[...] man has become kinder as a result of civilization; consequently, he’s becoming less bloodthirsty and less inclined to war[...]. Just look around: rivers of blood are being spilt, and in the most cheerful way, as if it were champagne[....]. Civilization merely promotes a wider variety of sensations in man and . . . absolutely nothing else. And through the development of this variety man may even reach the point where he takes pleasure in spilling blood. Why, that’s even happened to him already.
There are three levels to the figurative language in this sentence. First, the blood spilt in a war is compared to rivers using a metaphor. The blood is a river with the sheer amount of blood being spilt. Second, the narrator uses a simile to compare the rivers of blood to champagne, showing that it seems to flow in celebration, as champagne does. Third, it is situational irony, given that it seems that people would mourn that much blood flowing, but they celebrate it and encourage more blood to flow. It is the opposite of what one would expect in that situation.
The layers of figurative language here serve to show the impossibility of understanding human nature for what it is. It seems inconceivable that people would simply kill one another for the fun of it and celebrate that destruction, but that is exactly what the narrator is witnessing. He distances himself from the destruction and understands it through many layers of metaphor, simile, and irony.
In Part 2, Chapter 6, the narrative uses situational irony when The Underground Man describes his conversation with Liza:
“Oh, I’m not interrogating you. What do I care? Why are you angry? Of course, you may have had your own troubles. What’s it to me? Just the same, I’m sorry.”
“For whom?”
“I’m sorry for you.”
“No need . . . ,” she whispered barely audibly and stirred once again.
That provoked me at once. What! I was being so gentle with her, while she . . .
As the reader has witnessed The Underground Man berating and judging Liza for pages because of her life choices, the last thing they would expect is for him to refer to his words as "gentle." Readers can see that he is pressuring her with all of his rhetorical questions, demanding to know why she feels the way she does and giving a non-apology when she asks him about it. This moment is therefore ironic, as the reader would expect him to be aware that he is treating her poorly, but he instead says the unexpected: that he is treating her with gentleness.
This irony shows how The Underground Man does not fit in with society. He believes he is being gentle with Liza and understanding with other people, but he is in fact being abrasive and rude. This trait, on top of other discontent with Petersburg society, leads him away from society and to the underground.
In Part 2, Chapter 8, The Underground Man describes his servant, Apollon, treating him quite poorly in a moment of situational irony. As Apollon is the servant, the reader would expect him to defer to The Underground Man, but The Underground Man describes it as being the other way around:
[Apollon] treated me quite despotically, spoke to me exceedingly little, and, if he happened to look at me, cast a steady, majestically self-assured, and constantly mocking glance that sometimes infuriated me. He carried out his tasks as if he were doing me the greatest of favors.
The Underground Man can't fire him, and Apollon holds this power above him, being in control in their relationship. The narrator feels out of place in contemporary society and thinks he is entirely too intelligent and unfit to live as most people do. Ironically, the place that he seems to be the most subservient is his own home, where his servant controls his actions, instead of the other way around. This situational irony signals a role reversal of typical society in The Underground Man's home. In the one place where The Underground Man is supposed to find respite from the world (in his eyes), he is again seen as lesser.
In Part 2, Chapter 9, The Underground Man rebukes Liza after she comes to visit him despite caring for her, describing the situation using situational irony:
My eyes gleamed with passion; I pressed her hands tightly. How I hated her and felt drawn to her simultaneously!
The Underground Man understands how his insults have and continue to hurt her, and on the one hand, he wants to make her upset. He has a deep-seated hatred for her, but he continuously returns to her, eventually inviting her to his home and hoping she never appears (although she does). He wants to continue hurting her while staying in her vicinity.
It is ironic, then, when the narrator says that he hates her while feeling drawn "drawn to her." He contradicts himself with his opinions of her. This signals a larger facet of The Underground Man's personality that he ignores: the desire he has to connect with other people despite his simultaneous revulsion towards them. This is also evident in his attempts to get to know Simonov and his friends, even though he simultaneously derides them. He wants to connect with other people while still staying true to his antisocial principles and thinking himself more intelligent than them.