What validity do I need on my Irish passport for overseas travel?

This depends on where you're travelling to. 

European Union

Your Irish Passport must be valid up to your return date.

United States

Your Irish Passport must be valid up to your return date. And you must also get an Electronic System for Travel Authorisation (ESTA) under the Visa Waiver Programme for entry into the United States. You can find more information on the US Embassy in Ireland's website.

Canada

Your Irish Passport must be valid up to your return date. You must also get an Electronic Travel Authorization (eTA) for entry to Canada. You can find more information on the Government of Canada’s official website.

All other countries

The passport validity required for countries outside of the European Union and the United States varies greatly so contact your travel agent or the embassy of the country you're travelling to for the most up-to-date requirements.