We hear about Hurricanes, Tornadoes and Earthquakes all over the new world. How did the settlers deal with them and were there any instances of an almost total wipeout?
Before weather forecasting, storms blew in with no warning -- routinely catching ships at sea, for example. There are extensive records of this, and treasure hunters in particular have looked for Spanish gold fleets where on more than one occasion ships sank in the storms. A particularly famous treasure fleet that was hit by a hurricane sank the Nuestra Senora de Atocha in 1622 off the Florida Keys-- the treasure from this was recovered and sold by treasure hunter Mel Fisher and colleagues.
North American hurricanes are less frequent than Caribbean, but the Pilgrims were famously blasted by a devastating hurricane in 1635, a storm which is often called "The Great Colonial Hurricane".
William Bradford of Plymouth described it
Such a mighty storm of wind and rain as none living in these parts, either English or Indian, ever saw, It blew down sundry houses and uncovered others ... It blew down many hundred thousands of trees, turning up the stronger by the roots and breaking the higher pine trees off in the middle.
Similarly, John Winthrop
The wind having blown hard at S. and S.W. a week before, about midnight it came up at N.E. and blew with such violence, with abundance of rain, that it blew down many hundreds of trees, near the towns, overthrew some houses, and drove the ships from their anchors. The Great Hope, of Ipswich, being about four hundred tons, was driven aground at Mr. Hoffe’s Point, and brought back again presently by a N. W. wind, and ran on shore at Charlestown. About eight of the clock the wind came about to N.W. very strong, and it being then about high water, by nine the tide had fallen three feet. Then it began to flow again about one hour, and rose about two or three feet, which was conceived to be, that the sea was grown so high abroad with a N.E. wind, that, meeting with the ebb, it forced it back again. This tempest was not so far as Cape Sable, but to the south more violent, and made a double tide all that coast…The tide rose at Narragansett fourteen feet higher than ordinary, and drowned eight Indians flying from their wigwams.
One hurricane is thought to have played an indirect role in the extinction of a colony -- a hurricane in 1565 is given credit for the victory of the Spanish over the French in Florida. It's not so much the damage done to the colony itself, but rather the destruction of French naval vessels under the command of Rene Goulaine de Laudonnière left the Spanish with a free hand to conquer the French Huguenot colony at Fort Caroline.
Earthquakes are relatively uncommon in Eastern North America-- the Pilgrims didn't experience a significant one, so far as I'm aware. The largest quake East of the Mississippi in American history were the New Madrid quakes of 1811-12. This is long after the Pilgrims, obviously-- but did a lot of damage.
The most significant Western quake for which we have native American oral traditions -- not witnessed by Europeans, nor recorded at the time-- was a giant quake in the Pacific Northwest, very much a model of the it'll-come-some-day "Big Rip" in the Cascadia Subduction Zone. This massive quake hit in 1700, and was remembered in native American oral traditions more than a century later; it blasted the coast of Washington and Oregon, leaving evidence which is still visible today, forests near Grays Habor, Washington killed by the flood of saltwater in the tsunami. Indeed it was so powerful that the tsunami it triggered crashed into Japan on the other side of the Pacific. . . in Japan this was known as "the orphan tsunami", as they could find no local earthquake to have triggered it-- the triggering quake was thousands of miles away across the North Pacific.
Settlers and native Americans "dealt with" natural disaster as best they could. Ships at sea sank and people drowned. Buildings collapsed and were rebuilt, or not. There was obviously little or no warning for any of these events, so there was little to do except one's best.
As to the frequency of hurricanes, there's a new discipline of "paleotempestology"-- it appears that hurricanes were a bit more frequent from 3,800 to 1000 years ago; the period since then seems to be on the quieter side relative to those very long term geologic evidence. It does seem that extreme weather events are becoming more common with a warming climate in the late 20th early 21st century.
Sources:
New records of Atlantic hurricanes from Spanish documentary sources
Storm Tides in Twelve Tropical Cyclones (including Four Intense New England Hurricanes)
The orphan tsunami of 1700—Japanese clues to a parent earthquake in North America
The Great Carolina Hurricane of 1752
Storm Hazard and Slavery: The Impact of the 1831 Great Caribbean Hurricane on St Vincent