It's a brilliant song. In which ways is it odd though? I've always thought of it as just a classic 60's pop song. Listening again nothing jumps out as particularly unusual.
This might be referenced in one of the replies but basically 1) it doesn’t have the normal verse-chorus structure, 2) not really any drums, 3) the chord progression don’t follow an obvious pattern for the time and genre, and 4) the end just fades out where you can imagine it simply continuing forever. I really like the song, and maybe it stands out as a favorite because of these features like someone commented above. I just wanted to point out that it’s unusual unlike nearly every other pop song.
One more. Most of the song is in triplet swing, but there's a harpsichord(?) interlude in straight 8th-note feel, that's also completely harmonically disconnected from the rest of the song.
8-Bit goes into some of the unusual music theory of God Only Knows while talking about the (equally unexpected) a cappella cover in Bioshock Infinite - https://www.youtube.com/watch?v=9p-GFTfGdLE
