ESB Networks says that power has been restored to all but around 50 customoers.
The affected areas include the Midlands, counties Donegal, Westmeath and Sligo.
An ESB spokesman said the majority of customers in the northwest who had their supply disrupted earlier have now been reconnected.
ESB Networks say they have repair crews out in the affected areas and hope to have power restored later tonight or early tomorrow morning.
Met Éireann said southwest winds this evening will reach speeds of around 80km/h, with gusts of up to 130km/h. The most severe winds are affecting exposed parts of Connacht and Ulster.
It has also warned of coastal flooding and 'exceptionally high seas' along the western seaboard, due to the high tides.
Motorists have been warned of dangerous driving conditions in many parts of the country.
AA Roadwatch warned road users to take particular care on exposed roads and in high-sided vehicles.
P&O Ferries cancelled this afternoon's 1500 Dublin to Liverpool sailing as well as the 0300 sailing leaving from Liverpool tomorrow morning.
This morning's 8am Aer Arann flight from Carrickfinn (Donegal Airport) to Dublin was also cancelled due to severe weather.
In Donegal, emergency services dealt with a fallen tree at Glenconwall between Ardragh and Glenties.
The Harry Blaney bridge, which spans Mulroy bay in north Donegal, is closed until further notice due to weather conditions.
The high-level, multi-span bridge links the Fanad and Rosguill peninsula and the decision to close it was taken by Donegal County Council.
The 'Tor Mór' Tory Island Ferry will not sail today.
A number of roads were blocked by fallen trees around the country, but AA Roadwatch is reporting no major incidents related to the weather this evening, although motorists are still being urged to drive with care.
Schools on Arranmore Island off the Donegal coast have been closed because of the severe weather.
Ferry services to the island are suspended as they are unable to leave Burtonport Pier on the mainland due to high winds and rough seas.
Meanwhile, construction of exhibition tents was suspended on the site of the National Ploughing Championships because of high winds in Athy.
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