How new airplanes get in contact with ATC while flying in remote areas? Do they use VHF datalink (VDL) ?
Planes in the North Atlantic with the latest equipment as you ask would use VDL only within line-of-sight. Otherwise they would use satcom or HFDL (HF data link) for data comms.
Data communications will be via CPDLC or ACARS. For voice communications there is also a satcom voice option. There is also ADS-C for tracking, which is mandatory for certain flight levels.
Pilot-to-pilot voice communications to relay information or during emergency is also available on 123.45 and 121.5.
Further reading and source: ICAO NORTH ATLANTIC OPERATIONS AND AIRSPACE MANUAL