The storm has cut electricity to nearly 3000 homes, downed trees and flooded roads as it nears the territory.
At 10 am New Caledonia time it was situated at 19.5 degrees south, 162.6 degrees east about 110 kilometres west of Belep.
Oma is moving south westwards at 15km/h.
New Caledonia's weather service said gusts of up to 140 kilometres an hour had been recorded at Belep and Poingam
Oma is expected to strengthen slightly as it moves away from the territory.
Heavy rain and strong winds of up to 150 kilometres an hour in the far north are expected.
