(Aside: I did not know the word 音物.)
One of the meanings of the kanji 音 is “message,” that is, a piece of information sent from one person to another. 音信 (as in 音信不通) and 福音 seem to be the most common examples of 音 with this meaning. The reason 音物 (present; often refers to bribe) contains kanji 音 because a present is something which is sent from one person to another.
It is the best to look up a 漢和辞典 (a dictionary which explains kanji letters in Japanese) for questions like this, but the Daijisen dictionary, which is available online (linked above), contains entries for common kanji letters and comes in handy here.