When you say "medieval Irish society" do you mean medieval Irish history in general? Or more specifically social history - how the various groups in society were composed and how they interacted with one another? Is there any time period or area or topic in particular you're interested in? Part of the problem with medieval Irish history of course is that there aren't a huge number of people writing about it, so if there's a particular thing you're interested in, the most recent thing written about it could easily be 50 years old because no-one's gotten around to re-examining it. There's also a huge amount of insularity and conservatism, particularly in methods and on the theoretical side (because most of the work published in the 1960s and 70s was iconoclastic, some elder statesmen seem to have assumed that's enough, no need for any more new ideas): this is changing somewhat, but very slowly. There is also still quite a lot of politics in medieval Irish history, especially older works, so watch out for that (especially anything concerning the Ango-Norman invasions and colonies).

All of those caveats firmly in place, here's some starting points, at least:

• Thomas Charles-Edwards, Early Christian Ireland, (Cambridge, 2000): This is your best one-stop-shop for early medieval Ireland, with lots of social stuff: kinship, laws, the church etc. It's very thorough and academic and can be quite heavy in places.

• Seán Duffy, Ireland in the Middle Ages, (Dublin, 1997): Nice, easy, very readable introduction to medieval Ireland after 1000, though it might not have enough detail for what you're looking for.

• Art Cosgrove (ed.), The New History of Ireland, II: Medieval Ireland, (Oxford, 1987): Much more dated than its year of publication would suggest, it's still got useful overviews on a variety of topics though.

• Katherine Simms, From Kings to Warlords (Woodbridge, 1987): Great in-depth, and surprisingly readable, study of Gaelic society in Ulster in the later Middle Ages.

• Kenneth Nicholls, Gaelic and Gaelicised Ireland in the Middle Ages, (Dublin, revised ed., 2003): The standard book on Gaelic Ireland after the Anglo-Norman invasion.

• Brendan Smith, Crisis and Survival in Late Medieval Ireland (Oxford, 2013) and Colonisation and Conquest in Medieval Ireland (Cambridge, 1999): More narrowly focused than their titles suggest, these are nice case studies of the English impact on the colony of Louth, which have some nice bits about colonial society.

Hopefully that should get you a start at any rate! If there's anything else you'd like a more detailed recommendation on, I'll do my best. It's not really my area, but I read quite a bit about it at undergrad level and still have a lot of friends who work more seriously on it, so I could hit them up if need be.