What is Mr. O’Connor’s job, and why is he not doing it?
Mr. O'Connor's job is to go from door to door trying to rally support for the political candidate he works for, Tricky Dicky Tierney. The reason he isn't doing his job during this story is that the weather is bad, so he's staying inside.
We find this out early on in the story, in the eleventh paragraph:
Mr O'Connor had been engaged by Tierney's agent to canvass one part of the ward but, as the weather was inclement and his boots let in the wet, he spent a great part of the day sitting by the fire in the Committee Room in Wicklow Street with Jack, the old caretaker. They had been sitting thus since the short day had grown dark. It was the sixth of October, dismal and cold out of doors.
As you can see in the text, O'Connor's specific job is to "canvass one part of the ward." What this means is that he is supposed to walk around town, knocking on doors, talking to people to try to get them to support Tierney as he's running for political office. We assume that he's also supposed to be passing out cards with this text on them:
Mr Richard J. Tierney, P.L.G., respectfully solicits the favour of your vote and influence at the coming election in the Royal Exchange Ward.
However, because it's raining, it's not a good day for doing this work, which requires being outside. So, O'Connor is relaxing indoors by the fire instead, smoking cigarettes, and using those cards to light his cigarettes--which reveals the utter lack of respect that O'Connor feels toward his employer, Tierney.
The fact that O'Connor is basically doing nothing all day rather than the work he was hired to do helps us start to understand one of the themes of this story, a common one in James Joyce's short works of fiction: the stagnation of life. (You can read more about that theme here.)