Although many African-Americans moved from the South to the North in the period from 1870s-1930s, and probably almost as many whites did the same, there seem to be few songs about the exodus. The thread on secular African-American music caused me to wonder about their scarcity.
I would especially like to find folk songs or folk versions, both Black and White.

The parlor song "Going from de Cotton Fields," 1879, by Thos. P. Westendorf, entered White folk song repertoire. It has been sung by Grandpa Jones, and Bob Walker recorded it for the Library of Congress in 1937; the Carter Family sang a modified version.
It was sung by the Gilbert Family of Arkansas. Their version:

GOING FROM DE COTTON FIELDS

1
I'se a goin' from de cotton fields, I'se a goin' from de cane
I'se a goin' from de old log hut dat stands down in de lane
I'se gwine to join de expedition headed for 'de Norf
And de boat is on de ribber dat's gwine to take me off.

Chorus:
I'se goin' from de cotton fields and oh it makes me sigh
For when de sun goes down tonight I'se gwine to say goodbye.

2
They say dat up in Kansas so many miles away
De colored folks is flockin' round and gettin' better pay
I don't know how I'll find it dere but I is bound to try
So when the sun goes down tonight I'se gwine to say goodbye.

4
I dread to leave de dear old place where I was borned and bred
To leave de friends dat I have made and de graves of dem dat's dead
De flowers dat bloom on Massa's grave will miss de tender care
No hands like mine will take de pains to keep dem bloomin' dere.

4
Now Dinah she don't wanta go, she says she's gettin' old
She says she's 'fraid we'll freeze to death de country am so cold
But I'se bound to help my chillun some befo' I'se called to die
So when de sun goes down tonight i'se gwine to say goodbye.

5
I'se sold de old log cabin and de little patch of ground
Dat good old Massa gave to me when de Yankee troops came down
My heart is sad and sore now, de tears are in my eyes
For when de sun goes down tonight I'se gwine to say goodbye.

With musical score, pp. 186-187, Appendix One. Robert Cochran, 1999, Singing in Zion. The University of Arkansas Press.

A similar version of Westendorf's song has been collected in Alabama:
"I'm Gwine from the Cotton Fields," pp. 107-108, with music, Robert W. Halli Jr., Ed., 2004, "An Alabama Songbook, Ballads, Folksongs and Spirituals Collected by Byron Arnold."