There aren't too many songs about actual battles, but dozens of political songs and ballads from the various factions. Thomasson collection in BL, 'Ratts Rhimed to death', 1660, Rump'; 1662. M. Parker's "When the King enjoys his own again" (Percy Folios MS, tune on my website); "Fain I would" on my website (ZN833, broadside ballad index, tune on my website); "Fair Fidelia, tempt no more" (ZN840) on my website is the non-political version, but you can click on to the political version from the notes there (Scarce Songs 1). The one commonly know as 'The Blackbird (1651) has even been collected in the US (ZN69, 17th and 18th centruy tunes on my website). A search thorugh my broadside ballad index and H. E. Rollins' 'Cavalier and Puritan' will turn up others. Joseph Frank's 'Hobbled Pegasus', 1968, is a catalog of anonymous songs and poems of the period 1641-1660.