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.