Getting from Oviedo airport to Luarica

This response assumes you mean Asturias Airport to Luarca.

Aena manages Asturias Airport OVD
http://www.aena.es/csee/Satellite/Aeropuerto-Asturias/es/Inicio.html

Renfe Feve train provides service from Santiago de Monte to Luarca. See Renfe site click the FEVE button.
http://www.renfe.com/EN/viajeros/

ALSA bus provides service from the same place under the name Carcedo to Luarca.
https://www.alsa.es/en/

The station is two km from the airport ... so take a taxi or walk.

ALSA provides service from Asturias Airport to Gijon, Oviedo, Aviles, but not Carcedo or Luarca ... go figure.