[1] Oliver started his career with local club Breiðablik before signing with AGF in Denmark when he was 16 years old.
In 2014, he moved back to Breiðablik to start his senior career.
[2] On 25 July 2017 he signed a three years contract for Norwegian side Bodø/Glimt.
Oliver made his first senior international appearance on 17 November 2015 in a match against Slovakia, when he came on as a substitute for Jóhann Berg Guðmundsson with ten minutes left of the match.
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