We study Old Norse in school starting at 16 years old. It might be a stretch to say we "understand" it but most icelanders could get the gist of what was being conveyed.
The texts I remember being taught (just from the top of my head, I hope other icelanders can add to this list): Gylfaginning, Völuspá, Brennu-Njáls Saga, og Egils-saga.
Since old germanic influenced old norse and then old norse influenced old english highly I'm not surprised you were able to understand a sizable portion of it. But I know from my girlfriend that there are many 'old' german words not in common usage that she was able to use to help with her icelandic.