The term you are looking for is "parlor music" (or "parlour music"), which was the most popular style of music in western Europe and North America in the 19th and early 20th centuries. It's a difficult genre to define because the type of music is so broad. Basically, it means music that was commonly played and sung in the home. It's the same sort of music you would have heard in a tavern. The instrument of choice was the piano, which usually was located in the parlor. It was disseminated by means of sheet music, which could be purchased from book sellers, dime stores, instrument vendors, certain publishing houses that marketed by mail to the general public, "music houses" (stores that sold nothing but sheet music calibrated for every type of instrument and choral singing), or purchased from music teachers. Many public libraries also carried books of bound sheet music.

The content derived from many sources. Ballads were adapted from traditional folk songs such as "Johnny Has Gone for a Soldier," "Sweet Betsy from Pike," "The Three Ravens" (which is very old and was first documented in 1611 in Ravenscroft's :Melismata"), and Barbara Allen (which exists in literally hundreds of versions—ninety-eight being documented in Virginia alone). Music for the home was also composed by individuals. For example, "Bendemeer's Stream" was a popular Irish folk tune for which Thomas Moore wrote lyrics. Lady John Scott composed lyrics for "Loch Lomond," usually described as "a Jacobite Air." The compositions of Stephen Collins Foster were especially popular. (Foster composed more than two hundred songs, many of which are still well-known, such as "Jeanie With the Light Brown Hair," and "Beautiful Dreamer.") Music from operettas and "light opera" were also widely played and sung. The compositions of Victor Herbert (e.g., "Gypsy Love Song") and Sigmund Romberg ("One Flower Grows Alone in Your Garden") are examples of this type of music.

Some works commemorated historic events. "Joe Hill" recounts the story of labor organizer Joe Hill who was executed in 1915 on what may have been a false charge of murder. (The lyrics were written by Alfred Hayes and the music by Earl Robinson.)

Songs of the American Civil War remained popular well into the 20th century. "The Battle Cry of Freedom," "All Quiet Along the Potomac To-Night," "When Johnny Comes Marching Home" and "Battle Hymn of the Republic" were particularly well-liked.

References:

The best reference work for music of all types is "Groves Dictionary of Music & Musicians," (1926), published in six volumes. Unfortunately, this is out of print and hard to find. The updated version, "The Grove Concise Dictionary of Music" (1988) is more widely available from used book dealers or from public libraries.

Old sheet music is still obtainable and individual song books can be purchased from used book sellers. "The Fireside Book of Folk Songs," Boni and Lloyd (1966) is more than a collection of sheet music. It also contains articles describing the types and origins of the songs and notes which were particularly popular as parlor music.

"The Civil War Songbook," Crawford (1977) contains a lengthy article on the sources of Civil War music which discusses the continuing popularity of the songs. The book also provides sheet music for 37 songs, including both Federal and Confederate compositions.