Sgt Robert Brown, from South Molton Police Station, said police were dealing with “numerous trees down across our roads, landslides and general debris”.
The Tamar Bridge, which connects Devon and Cornwall, was closed to high-sided vehicles because of the strong winds.
Stuart Hughes, from Devon County Council, said it was a busy morning and night and they had faced “very challenging conditions”.
“It’s very dangerous out there,” he said.
Great Western Railway stopped running trains between Plymouth and Penzance on Saturday morning because of track closures.
Nick Million, from Network Rail, said: “We have multiple trees down and multiple obstacles that have blown on the lines.”
Newquay Airport closed because of the conditions, with flights expected to resume on Sunday.
However most flights were taking off as normal at Exeter Airport, except to and from the Channel Islands.