Epikhodov offers pretty much straight comic relief from his first entrance in Act 1, when he "enters with a bouquet. He wears a short jacket and brilliantly polished boots which squeak audibly. He drops the bouquet as he enters, then picks it up" (1.10). As an accountant for an estate with no money, his very presence is kind of a joke. And he's a consistent source of slapstick humor and malapropisms (words made up or used incorrectly). As Dunyasha notes early on, "he's a nice young man, but every now and again, when he begins talking, you can't understand a word he's saying…He's an unlucky man; every day something happens. We tease him about it. They call him 'Two-and-twenty troubles'" (1.18).
Epikhodov's a clown, sure, but he also serves a deeper purpose in the play. In his unrequited love for Dunyasha, he's an unfortunate victim of the "upward mobility fever" infecting the younger working-class characters. Yasha's travels and gentlemanly pose attract Dunyasha, who fancies herself a quasi-lady. Epikhodov seems beneath her now. He works hard to regain her attentions and mostly fails:
EPIKHODOV. I'm an educated man, I read various remarkable books, but I cannot understand the direction I myself want to go—whether to live or to shoot myself, as it were. So, in case, I always carry a revolver about with me. Here it is. [Shows a revolver.] (2.10)
There's something both amusing and sad about his pathetic attempts to win Dunyasha. To look cool, he apes Yasha's impertinence in Act 3. He plays billiards, breaks a cue, and defies his boss, Varya. Everything turns out OK for Epikhodov, however. When Lopakhin buys the estate, he leaves Epikhodov in charge:
LOPAKHIN. Yes, all, I think. [To EPIKHODOV, putting on his coat] You see that everything's quite straight, Epikhodov.
EPIKHODOV. [Hoarsely] You may depend upon me, Ermolai Alexeyevitch!
LOPAKHIN. What's the matter with your voice?
EPIKHODOV. I swallowed something just now; I was having a drink of water. (4.108-109)
What is Lopakhin thinking? Perhaps it's Chekhov's final comment on the age of gracelessness descending on the estate.