[details=“English Translation”]When my little brother doesn’t want to listen, he covers his ears and starts singing.
[/details]
According to Google Ngrams, “se tapa los oídos” is far more common:
se tapa las orejas 0.0000003290%
se tapa los oídos 0.0000025846%
It might be a regional thing. For me “las orejas” sounds more natural
It would be interesting to know which region is your frame of reference. 
Mine is the Madrid region, but that was ages ago.
Barcelona (and here some extra characters otherwise to comment wont be accepted : D)
In catalan I say tapar-se les orelles, maybe that’s the reason (if you are a native Catalan speaker) you use orejas instead of oídos. Although in Spanish it sounds more natural to me taparse los oídos.
That might indeed be the reason