Old English sang "voice, song, art of singing; metrical composition adapted for singing, psalm, poem," from Proto-Germanic *sangwaz (cf. Old Norse söngr, Norwegian song, Swedish sång, Old Saxon, Danish, Old Frisian, Old High German, German sang, Middle Dutch sanc, Dutch zang, Gothic saggws), from PIE *songwh-o- "singing, song," from *sengwh- "to sing, make an incantation" (see sing (v.)).
Phrase for a song "for a trifle, for little or nothing" is from "All's Well" III.ii.9 (the identical image, por du son, is in Old French. With a song in (one's) heart "feeling joy" is first attested 1930 in Lorenz Hart's lyric. Song and dance as a form of vaudeville act is attested from 1872; figurative sense of "rigmarole" is from 1895.
Something or someone bedraggled, perhaps due to weather (1928+)