The party that is described during this great short story--perhaps one of Joyce's best--details the opinions of the assembled masses concerning a number of different issues. However, if you are looking for politics, you need go no further than the conversation Gabriel has with Miss Ivors concerning the fact that he writes for The Daily Express, a newspaper opposed to Irish liberation. This was of course a massive issue of the time and Gabriel wants to give some kind of "grandiose response" to Miss Ivors but is unable to.
Concerning art, when Gabriel wanders to the wall above the piano he comments on the paintings that he sees there:
A picture of the balcony scene in Romeo and Juliet hung there and beside it was a picture of the two murdered princes in the Tower which Aunt Julia had worked in red, blue and brown wools when she was a little girl.
Lastly, if you are looking for references to religion, consider Aunt Kate's reference to the Pope and his decision to dispose of the women in the choirs in Rome:
-I know all about the honour of God, Mary Jane, but I think it's not at all honourable for the pope to turn out the women out of the choirs that have slaved there all their lives and put little whipper-snappers of boys over their heads. I suppose it is for the good of the Church if the pope does it. But it's not just, Mary Jane, and it's not right.
So, these are just some of the references to religion, art and politics in this excellent short story. You might want to go and re-read it now to see if you can identify any more references. Good luck!