Depends a great deal on what happened to the home rule/independence movements and even then I couldn't say with any sort of certainty.
Pre-1918 o/c the island was strongly Nationalist with the exception of NE Ulster and the Trinity seats. IIRC, after the foundation of the Irish Parliamentary Party in 1882, Westminster elections here were effectively very simple matters with 80 something IPP MPs returned and the remaining 20-ish (?) Conservatives returned from NE Ulster and Trinity College (until the Unionists came about in 1905 when they simply took over those seats and took the Tory whip).
Pre-1982, the Home Rule League was much the same as the IPP in terms of electoral success, but had more competition from the Liberals splitting some seats allowing more Tories in. The last election when no Irish party won (or really contested I suppose) seats in Westminster was 1868, when the Liberals won comfortably. Earlier than that... I don't really know much about in electoral terms.
As for today, if the only options on the ballot were Con; Lab; and LibDem... I'd imagine Labour would do well or at least be very competitive in North Dublin; Cork City; Wicklow; Kildare; maybe Louth.
I could see plenty of LibDem votes in South Dublin, but beyond that...hard to say.
Conservatives...(assuming Nationalism not an issue) should do well in the North-West [Donegal; Cavan; Monaghan; Mayo; Leitrim...]
It's very hard to speculate. Somethings I don't really know...historically which party would do best in appealing to the rural vote - particularly small farmers and agri-labourers; how the country would react to abortion; and to involvement in another World War...
Throwing in a nationalist party and well, I can only judge on things like the previous returns for the various Nationalist parties pre-1922 (Sinn Féin; IPP; Home Rule League) which all dominated here.
It's very hard for me to imagine what Ireland would be like today without having gained independence 80 years ago; what the country would be like either as effectively devolved government - had the 3rd Home Rule Bill been implemented; or as simply just another part of the UK.
Anyhoo... population figures would be hidden around various parts of the CSO website, for example here are the
current county populations; and here are the
current constituency populations. I have no idea how many seats we'd have or how those additional votes would have affected the course of British and Irish history.