Houses once owned by ancestors - how do I go about learning more?

I've heard a statistic from a professional genealogist that only 2% of people prior to the early 20th century left wills. So unless your ancestors had a lot of land or were wealthy, there won't be one. And in more general circumstances, a lot of wills were destroyed in the 1922 four courts destruction. What does survive is in the National Archives and there are also public record office abstracts of wills and calendar books for each with a little summary. You also get some wills in the Registry of Deeds, which is what you want for a property search - just like today. If you're buying a property, your solicitor does a search in the registry of deeds going back a fair amount of time (my own newly built apartment had a search done of at least 120 years).

Before you go to the RoD, which is still a very Victorian setup sans computers, albeit with helpful staff and lovely surroundings, check in directories. Thoms for Dublin, Guys for Cork, Slaters/Pigots/Ferrars for the wider country. If it's a good sized property, it may well be listed in them and by checking every couple of years (Thoms starts about 1840s but there's other Dublin ones before it), you could build up a good link. Pearse St library has the best and easiest to access collection but they are also in the National Library and the new archives in Swords has a good selection.

Another option is the valuations office, in the same building as the GRO research room. Rates were paid until the 1970s, so you can search back an address in there. Griffiths would indeed be useful, but it may be too early for your information.