In the southern state, Victoria State Emergency Service crews responded to nearly 350 calls for help overnight, including more than 100 reports of building damage.
More than one-third of the call-outs were for the Warrnambool region, on the state's southwest coast.
The town recorded wind gusts of more than 100km/h on Friday morning, accompanied by widespread showers.
David Baker from VICSES told ABC TV there were also concerns about the possibility of coastal erosion as swells of up to 8m struck the state's coast.
"Stay home if you can; stay inside, have a Netflix binge," he said.
"Today is not the day to be out on the water."
There were 16,000 customers without power in Victoria at midday.
Wind gusts of about 80km/h hit Sydney late on Thursday and early on Friday, leaving NSW SES crews scrambling to respond to calls for help.
Some parts of Sydney and inland NSW were also hit with brief, heavy downpours, although many areas were spared from significant rain.
The NSW SES responded to more than 200 calls across the state after midnight on Friday, about a quarter of which were in Sydney.
SES metro zone commander Allison Flaxman said the city's northern beaches region was among the areas hardest hit.
"Most of the incidents were for fallen trees, including some very large ones which blocked traffic and impacted powerlines," she said.
Three trees fell on one home in Frenchs Forest and firefighters were called in to help as more trees threatened to collapse on the property.
The homeowner told the ABC her family came outside the house about 1am due to the noise, just in time to see the trees topple on their garage.
Severe weather warnings remained in place on Friday afternoon across much of Victoria's south, including Melbourne, as well as parts of NSW and South Australia.
The Bureau of Meteorology said wind speeds of 142km/h were recorded at Thredbo in the NSW Snowy Mountains region, while similar speeds were noted nearby at Victoria's Hotham.
The bureau warned strong winds would reach the west Gippsland coast later in the afternoon on Friday, with strong winds also expected in the Snowy Mountains and NSW Southern Highlands, as well as the ACT.
Showers and small hail were possible for large parts of Victoria, South Australia and Tasmania.
The SES warned people to avoid travel if possible and to be wary of any hazards like floodwater or debris such as fallen trees.
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