Bridgend council said streets were sealed off due to falling roof tiles.
Elsewhere, the M4 was shut by a blown-over lorry, rail passengers have been facing cancellations, and Wales rugby fans flying back to Cardiff from Dublin have been diverted.
At its peak, about 3,700 homes had no electricity.
Over the course of the day Western Power Distribution has dealt with more then 5,000 power cuts in Blaenau Gwent, Bridgend, Cardiff, Carmarthenshire, Neath Port Talbot, Swansea, Rhondda Cynon Taff, Monmouthshire, Newport, Pembrokeshire, Swansea, Torfaen, Vale of Glamorgan and Ceredigion.
The storm was expected to clear by 18:00 GMT.
Damage was caused to a number of buildings - which led to the closure of streets around Bridgend town centre.
In Pembrokeshire, part of the roof of St Davids Fire Station was dislodged, while in Tenby, there were reports of unsafe structures.
On the M4, a lorry which blew over on the M4 between Junction 37 (Pyle/Porthcawl) and Junction 38 (Margam) has been removed but the motorway reopened after repairs were carried out.
Strong winds also closed the M48 Severn Bridge in both directions, with it later reopening with driving restrictions in place.
Rail services have also been disrupted across Wales.
First Great Western advised rail passengers not to travel between Cardiff, Bristol, Gloucester, Westbury and Taunton.
And Arriva Trains Wales said there were severe delays on services to west Wales while all lines at Cardiff Queen Street station were temporarily blocked on Monday afternoon.
But the Cambrian line which runs between Aberystwyth and Shrewsbury has reopened.
Rugby fans due to fly back to Cardiff Airport after the Six Nations 16-all draw with Ireland in Dublin were diverted to Birmingham, Bristol and Manchester while other flights were also affected.
The highest wind speed of 83mph was recorded at Pembrey, Carmarthenshire followed by 82mph at Mumbles, according to official Met Office data.
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Winds of up to 83mph shut several parts of a town centre as Storm Imogen battered south Wales and caused power cuts to thousands of homes on Monday.