Hallow Eve is, apparently the same thing as Halloween (the day before All Saints Day).
I don't know what Ivy Leaf refers to. Perhaps some context would help.
The Ivy Leaf in English folklore has long meant friendship or constancy. It was (for that reason) the symbol of Charles Parnell, the Irish leader of The Irish Nationalist Party, a precursor of the IRA (but the last gasp of democratic struggle against British rule in Ireland) in the latter part of the 19th Century. Parnell achieved some success (even having an MP elected in Liverpool, a redoubt of Irish immigrants in England), but he was discredited amongst the Catholic Irish for having an affair with a married woman.
"Dubliners" is a collection of short stories, the one in question being "Ivy Day in the Committee Room" - 'Ivy Day' in Ireland is the anniversary of Parnell's death of a heart attack in 1891. In Joyce's story, the man with an ivy leaf in his hat is showing solidarity with Parnell.