Waxie's Dargle

As others have said, aul wan is Dublin slang for a woman, your aul wan is your mother or your wife, depending on context, in this context it's wife.

The waxie's dargle was an annual summer excursion/picnic near Ringsend in south Dublin. It could also have a second meaning as rhyming slang for booze. Waxie's dargle rhymes with gargle which is Dublin slang for alcohol.

Monto was a notorious red light district in Dublin in the late 19th and early 20th century, The area got its name from Montgomery Street (now called Foley street) which is just off O'Connell Street/Talbot Street/Amien Street.

A farthing was the smallest unit of currency in the old punds/shillings and pence system used in Britain and Ireland, a farthing was half a halfpenny. A half crown was a more valuable coin worth 2 shillings and sixpence.

Capel Street is another Dublin Street, it is on the opposite side of O'Connell Street from the Monto running roughly parallel to O'Connel Street it used to have a lot of pawnbrokers and money lenders shops.

So in the first verse the first woman asks the second if she's going to the Waxie's Dargle, the second says she has no money so she went up to Monto to see Uncle McArdle but he wouldn't give her half a crown. So basically she went to the red light district to make some money but was not successful.

The second verse is about going to the Galway Races, this time she goes to Capel street to pawn her husband's braces/suspenders but the Jewish moneylender wouldn't give her any money for them.

In the final verse the women have no meat so again go up to Monto to make some cash.

The chorus is about ordering a drink before they get thrown out of the pub, it's this that makes me think that the title might also be a rhyming slang reference to alcohol.

Monto was supposedly the biggest red light district in the early 20th century, Dublin was one of the poorest cities in Europe and the slums and tenements of Dublin were notorious for their poverty, it was common for poor women to pawn clothes and household goods to make ends meet and then when their husband got paid buy the items back, similarly many women would go to Monto to make a few shillings when times were tough.

My reading of the song overall is that the verses are the men discussing conversations between their wives and the chorus is a reminder to buy another drink before they get thrown out. Basically two drunk men in Dublin bitching about their aul wans in the pub (not realising or caring that one of the reasons the aul wans have to go to Monto or Capel Street to make some extra money is because the husbands are spending their wages in the pub)

The song Monto, which the Dubliners used to sing is also about this area and time (and makes a reference to the Waxie's Dargle in the first verse).