From the notes to the Penguin Book (1959):

"The Devil comes to fetch a farmer's wife.  The farmer is delighted.  But the shrewish woman behaves so abominably in Hell that the Devil is obliged to bring her back again.  The song, apparantly common all over the British Isles and frequently recorded in America, seems to embody a very old joke indeed.  Perhaps in early forms, the farmer had enlisted the Devil's aid in his ploughing, promising the soul of one of his family in return.  Most versions of this song have a whistled refrain, and this is not without sly meaning, for there is an old belief that whistling summons the Devil (hence the sailor's superstition that whistling aboard ship may bring on a storm).  Burns re-made a Scottish version of the ballad, and called it  The Carle o' Kellyburn Braes.  Mrs. Burns, speaking to a scholar of the way in which her husband altered folk songs, remarked: "Robert gae this ane a terrible brushing".  Our text is filled out with some verses obtained by Alfred Williams from David Sawyer, of Ogbourne, Wiltshire.  (Folk Songs of the Upper Thames, 1923).  A Dorset version is given in FSJ vol.III, p.131-2."  -R.V.W./A.L.L.

This version was collected by Ralph Vaughan Williams from H. Burstow of Horsham, Sussex, in 1903, and was first published in The Folk Song Journal, vol.II, p.184.

Child 278
@devil @marriage

Versions on the DT:

The Women Are Worse Than The Men  From Irish Street Ballads, ed. Colm O' Lochlainn, 1952.  No tune given.
The Devil And The Farmer's Wife  Transcribed from a record?  No tune.
Tee Roo  US version, with tune.
Kellyburnbraes  Robert Burns' version, with tune.
Devil And The Farmer's Wife  US version, with tune.

In the Forum:

Killieburn Brae   From a Dubliners songbook.
Auld Carle   (No source specified.)
The women are worse than the men  Mostly discussion, includes another version of Kellyburn Braes.

There are versions at Lesley Nelson's  Child Ballads  site:

The Farmer's Curst Wife  (The Devil and the Farmer)
Child version A
Child version B
Kellyburnbraes

Bruce Olson has the text of the earliest known broadside version at his website:

A Pleasant new Ballad you here may behold, How the Devill, though subtle, was gull'd by a Scold.  "Printed at London for Henry Gosson, dwelling upon London-Bridge neare to the Gate". Stationers' Register, June 24, 1630.

There is an entry at the  The Traditional Ballad Index:

The Farmer's Curst Wife

Other titles:

The Old Man under the Hill
The Devil and the Farmer's Wife
Give eare, my loving countrey-men
Old Lady and the Devil
The Farmer's Curst Wife
Little Devils
Randy Riley
The Old Woman and the Devil
The Farmer and the Devil
The Carle o' Killyburn Braes
The Battle Axe and the Devil

There are some broadside versions at  Bodleian Library Broadside Ballads:

The Devil in search of a wife  Printed between 1819 and 1844 by J. Pitts, 6 Great St. Andrew Street, Seven Dials, London.

A pleasant new ballad you here may behold, how the divel (through [sic] subtle) was guld by a scold  Printed between 1663 and 1674 for F. Coles, T. Vere, and J. Wright of London.

The Sussex farmer  Printed between 1819 and 1844 by J. Pitts, Toy and Marble Warehouse, 6 Great St. Andrew Street, Seven Dials, London.

These are large images.  The last is closest to the traditional versions.

Malcolm