It is understood that Ms O'Neill was driving on the R671 at about 11.40am yesterday between the villages of Clashmore and Aglish in Co Waterford when a branch fell on the vehicle and went through the windscreen.
In Cahir, Co Tipperary, a man in his 30s was killed in a chainsaw accident when he was trying to clear a tree downed by the wind.
Although ESB Networks says crews are working around the country to fix faults, there is no current time for restoration of service in the local area.
It was the worst storm to hit Ireland since the 1960s and you would have hoped for at least a period of calm weather.
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Meanwhile the Department of Education has announced that all schools will remain closed again tomorrow.
The Met Office has issued a yellow warning today, with spells of very windy weather and the potential for more power cuts.
Their forecast added: 'Some damage to buildings, such as tiles blown from roofs, could happen'.
Speaking about the issue an ESB spokesperson has said the South, South East, South West and parts of the Midlands are the worst affected.
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A reporter at the scene with the local TOLOnews agency said heavy fighting was ongoing on Tuesday. Fourteen Afghan security forces were killed and nine wounded when the vehicle exploded.
By late afternoon, approximately 360,000 electricity customers were without power as a result of over 3,200 individual faults on the network across the country.
'There's still a risk of gales and it's still strong enough to cause disruption, but a little bit down on what we have seen'.
Help from Northern Ireland and the rest of the United Kingdom is expected to be drafted in on Wednesday to help restore power, ESB, the Republic of Ireland's electricity network, said.
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