Met Éireann has issued a Status Orange wind warning for counties Donegal, Leitrim and Sligo.
It will come into effect from 4am until 8am tomorrow morning.
Met Éireann said it could cause further damage to already weakened structures, lead to fallen trees, damage power lines and possible power outages.
It will also cause very difficult travelling conditions and possible wave overtopping.
A Status Yellow wind warning for Clare, Kerry, Galway and Mayo will come into effect at 12am and will be in place until 12pm tomorrow.
A yellow wind warning for Dublin, Louth and Wicklow will come into effect at 6am and will expire at 12pm.
Northern Ireland will be under a yellow rain warning from 11am until 12pm and then a yellow wind warning will come into effect at 2pm and last until 12am.
Met Éireann is warning of difficult travelling conditions, debris, loose objects displaced, localised flooding and some fallen trees possible.
Earlier, a man was killed in a weather-related incident and about 174,000 properties are without power across the island of Ireland as Storm Amy brought widespread disruption.
The storm also brought localised flooding, fallen trees, transport disruption and school closures.
Met Éireann issued its highest-level wind warning in Co Donegal, where residents were advised to shelter in place between 4pm and 6pm.
The red wind warning meant fallen trees, damage to power lines, dangerous travelling conditions, structural damage and wave overtopping.
Gardaí said they were treating an incident where a man was seriously injured in Letterkenny, shortly after 4.15pm, as weather-related.
They later said he had died and his body was removed to the morgue at Letterkenny University Hospital, where a post-mortem examination will be carried out in due course.
The ESB said around 124,000 homes, farms and businesses across the State were without power.
The ESB said affected properties were predominantly in counties Galway, Mayo, Sligo, Roscommon, Leitrim, Cavan and Donegal.
It also warned that further power outages can be expected.
A spokesman said: "Crews will continue the restoration work for as long as possible this evening, but it is likely that the majority of customers will not have their power restored tonight due to the hazardous weather conditions and accessibility challenges."
Gusts of up to 130kph were recorded at Malin Head in Co Donegal at 3pm, while consistent wind speeds of up to 89kph were recorded elsewhere in the county at Finner Camp.
The most severe conditions were forecast for Co Donegal where a red wind warning was put in place.
National Directorate for Fire and Emergency Management director Keith Leonard said: "If I had one key message, it would be for that period from 4 to 6 in Donegal this afternoon, to ask people to shelter in place for that amount of time and to be very careful on the roads before that warning comes into place and after it's gone through."
Speaking on RTÉ's News at One, Mr Leonard said the storm will also feature "a lot of rainfall" and that fallen trees are likely to be an issue.
The conditions led to some flight cancellations in and out of the country's airports.
At sea and along the coast, there was also a red warning from Loop Head to Ceann Ros Eoghain to Fair Head between 2pm and 8pm.
Tomorrow, there will be further yellow warnings for wind in Dublin, Louth and Wicklow between 6am and noon, a combined wind and rain warning for Donegal, Leitrim and Sligo between midnight and noon and a wind warning for Clare, Kerry, Galway and Mayo also between midnight and noon.
Schools across a large part of Northern Ireland were advised to close early as the high winds brought disruption.
About 50,000 properties are without power in Northern Ireland and NIE Networks said there had been a "significant level of damage to the electricity networks" in the region.
It also said the number without power is expected to rise.
NIE Networks operations manager Alex Houston said: "Our incident management centre in Craigavon has been opened as have our local incident centres across Northern Ireland with staff across the company being escalated to assist with the response effort.
"We have mobilised additional call agents to deal with any queries customers may have regarding the repair process in their area."
A provisional October wind gust record for Northern Ireland was set as 148kmh winds were measured at Magilligan in Co Derry, the UK's Met Office said.
Flights and trains have been impacted and a number of roads were closed in the region due to fallen trees, including part of the M1.
Forecasters said there would be damaging winds with every county on the island under weather warnings tonight.
The UK Met Office said wind speeds could reach up to 130kph along the most exposed coastal areas of the island, with fallen trees and power outages among the potential impacts.
In Northern Ireland, a yellow wind warning was put in place for the entire region between 2pm and midnight.
A yellow rain warning is in place for the region until midday tomorrow, with the Met Office warning the flooding of homes and businesses is possible.
