Vanya's suicide comment (Verbal Irony)
Vanya comments wryly that "It's a perfect day. For a man to hang himself" (126). Here, he uses sarcasm—verbal irony—to express his bitter and cynical attitude on the world around him, making a glib comment on the supposed value of life.
Vanya's light (Verbal Irony)
Vanya's mother tells him, "You used to be a man of such firm principles, a shining example," and Vanya replies, "Oh yes, I've been an example of something all right, but I haven't shone" (125). This is an example of verbal irony: Vanya sarcastically repeats what his mother says and adds a twist to it, telling her that he is a light that lights up no one. A light, of course, should illuminate things, but Vanya only bears darkness.
Serebryakov (Dramatic Irony)
When Serebryakov tells Vanya, Sonya, and the rest of the household, "You should get down to work, gentlemen. What we need is a bit of action," it is an example of dramatic irony. He sincerely believes that he needs to tell these people who already work hard that they need to get to work; ironically, though, Sonya and Vanya already work extremely hard, while Serebryakov is the one who is idle and needs to be told to work. He does not have an understanding of his own character, but the audience surely does—and this is what makes it dramatic irony.
The Subtitle (Verbal Irony)
Chekov's subtitling the work "Scenes from Country Life in Four Acts" is ironic because it sounds serious, intellectual, and part of an older, more distinguished dramatic tradition, rather than an essentially plotless and languorous (albeit brilliant) play about rich people's complaints, grievances, and petty love affairs.