There is no contemporary indication of her parentage, but there several theories about her possible ancestry:
According to the Andalusian historian Ibn Hazm (994-1064), she was married to "Garcia, King of the Basques, from which Musa ibn Garcia was borned" (which would make this Oria the same person as Awriya binti Musa).
Historian and professor Antonio Rei suggested she might have been a granddaughter of Musa ibn Musa ibn Qasi (Rei, 44–45) (which would make this Oria a niece of the aforementioned Awriya binti Musa). The Banu Qasi were a Christian family who converted to Islam - see Conde Cassius (Qasi).)
Historian and genealogist Christian Settipani suggested she might have been a daughter of the aforementioned Awriya binti Musa and Garcia, King of the Basques. The latter would be a son of García Galíndez the Bad and his first wife Matrona, daughter of Aznar I Galíndez, count of Aragon (Settipani, 114)
Settipani also suggested she might have been a daughter of García Galíndez the Bad and another Aurea (who is usually named Nunila), his second wife, the daughter of Eneko Arista (Íñigo Íñiguez "Arista" of Pamplona) and sister García I of Navarre (Settipani, 114).
Settipani also suggested she might have been a daughter of Galindo I Aznárez, count of Aragon, and a granddaughter of Aznar I Galíndez and a third Aurea, who could be the daughter of the Duke Lupo II of Gascony and a sister of Oneca or Iniga, the mother of Eneko Arista (Íñigo Íñiguez "Arista" of Pamplona) and Musa Ibn Musa lbn Qasaw, Walí de Tudela, Huesca y Zaragoza (Settipani, 115).
Spanish Wikipedia (citing Rei) supports the theory she was daughter of Lubb ibn Musa (Lope ibn Musa) and Ayab al Billatyya, and a granddaughter of Musa ibn Musa and Assona Iniguez but says in a footnote that her parentage is not documented. Unsourced Internet genealogies most often identify her thusly.
