It's obscured by the writing system somewhat. The spelling system is derived from Old Norse and is very conservative. It's not at all indicative of how it's really pronounced. The written form is somewhat mutually intelligible with Icelandic, but the spoken language is not.
Underneath those æ and ð is a language that is oddly similar to English, like convergent evolution. It has undergone an extensive vowel shift (but in a different pattern). And also like English, it has also undergone extensive affrication (turned into ch/j) of the stop consonants and reduction of final stops and intervocalic stops. It has the same kind of stress - vowel reduction interaction that English has which just heightens the uncanny effect.
I came away with the impression that it is English's closest sibling language, aside from Dutch:
broðir "broh-wer" (brother), heyggjur "hoy-cher" (hill/height), brúgv "brukf" (bridge), sjógvar/sjós "shekvar/shos" (sea), skyggj "skooch" (sky/cloud), djópur "cho-pur" (deep), veðirinn "ve-vir-uhn" (weather). Rough pronunciations given between quotes; all examples are cognate with English!
There's an extended story reading by a native speaker here [1] if you want an example of what it sounds like. No idea what they're saying but it sounds pretty.
[0] https://annas-archive.org/md5/4d2ce4cd5e828bbfc7b29b3d03349b...