"Sure ting! Dat's me. What about it?" (Situational Irony)
When Paddy asks Yank rhetorically whether he would like to be bound to the ship's furnace like a part of the machine, Yank (in a tone the stage directions specify as “contemptuous”) accepts the seemingly unappealing idea. Instead of seeing Paddy's notion as an imprisonment, Yank sees it as an increase of his own power.
The Astonishment Caused by Paddy's Speech (Situational Irony)
Even though the coal stokers have been haranguing drunkenly and countering arguments with the blunt threat of force, when Paddy, a more senior worker among them, moans an elegy to the lost days of sailing and a more humane kind of working life, they do not continue in the same vein as before. Surprised at their own reactions, they listen with a certain quiet reverence uncommon to them.
Bells Sound the Work Shift (Situational Irony)
Even though Yank and the other stokers have been contemptuously boasting about their strength and independence, as soon as the eight bells sound (mechanically) to summon them to their shift at the stokehole, everyone suddenly loses their raucous confidence and files down to work like machines.
"How the black smoke swirls back against the sky! Is it not beautiful?" (Verbal Irony)
Mildred's first line in Scene Two, said with an “affected dreaminess,” seems deliberately calculated to annoy her aunt, whom she knows disapproves of her interest in such unwomanly things as industry and the workings of the ship's stokehole. The affectedness of her speech shows that Mildred is striking a deliberately ironic pose.