I heard somewhere that we speak a mild 'Elizabethan' English in the West of Ireland... no idea if this is true really.

Although my parents use some archaic words:

"Pass me yon cup please." (Yon as in yonder = that cup)

"It's a bully old day." (bully = good, grand)

"That's a quare setup." (quare = strange)

"Oh aye... that's right." (aye* = yes) *common in Northern Ireland / Scotland too

We use "woe" a lot. (woe = misery)

Em... that's it really I suppose.