From ICAO; AIR TRAFFIC MANAGEMENT (DOC 4444)
15.2 SPECIAL PROCEDURES FOR IN-FLIGHT CONTINGENCIES IN OCEANIC AIRSPACE
15.2.3 Weather Deviation Procedures
15.2.3.1 General
NOTE: The following procedures are intended for deviations around adverse meteorological conditions.
15.2.3.1.1 When the pilot initiates communications with ATC, a rapid response may be obtained by stating “WEATHER DEVIATION REQUIRED” to
indicate that priority is desired on the frequency and for ATC response. When necessary, the pilot should initiate the communications using the urgency call “PAN PAN” (preferably spoken three times).
15.2.3.1.2 The pilot shall inform ATC when weather deviation is no longer required, or when a weather deviation has been completed and the aircraft has returned to its cleared route.
15.2.3.2 Actions to be Taken When Controller-Pilot Communications are Established
15.2.3.2.1 The pilot should notify ATC and request clearance to deviate from track, advising, when possible, the extent of the deviation expected.
A call for weather deviation would go somthing like this:
"Blackjack 201, weather deviations required 20 miles right of track."