The Oxford English Dictionary describes "song" as:
1.(a) A short poem or other set of words set to music
(b) "singing" or vocal music (not necessarily lyrical)
(c) a musical composition suggestive of a song (ie, a catchy chorus that the words just haven't been written for yet)
2. The musical phrases uttered by SOME birds, whales and insects...
3. A Poem, especially one in rhymed stanzas.
In the meantime, it can be used to mean other things too depending on context:
1. ...for a song = very cheaply
2. on song = on form
3. a song and dance = a fuss
In North America, a long and pointless or evasive explanation can be called a song.
Its origins are apparently Germanic.
It's all in the dictionary.