Seems like a lot of obvious things have been missed.
Nina Simone - I shall Be Released I would kick things off with that.
Dylan has another song with the refrain "pity the poor immigrant", but I don't know of any good versions.
Woody Guthrie - Deportees, Sweeet Honey In The Rock did an accapela you can mash. I always liked the way Judy Collins did it. I can't imagine you doing this project with out this song. Another must.
Woody Guthrie - Pastures Of Plenty.
Woody Guthrie - Do Ray Me, about coming to California.
Blind Alfred Reed - How Can You Keep On Moving, again about American migrants, Ry Cooder covered it.
Violionaires - Salt Of The Earth, doesn't mention immagrants or jail directly, but a better Rolling Stones penned song than Gimme Shelter. Better captures the immagrant experience I think. The Violinaires version will make you cry.
By The Rivers Of Babylon - The ultimate coming to a new land song (though it is about slavery of course). Melodians are the classic, no? I heard Sweet Honey In The Rock do this live, if it is on lp there is your accapela.
Georgia Sea Island Singers - The one with the refrain "Before I'll be a slave I will be buried in my grave". I've heard Sweet Honey do this one as well. Either version would be accapela.
There are so many blues and country prison songs. The blues one I would look for is Parchment Prison Blues (also known as Baby Please Don't Go and Another Man Done Gone). The Folkways site should have some accapelas.
I think it is Keb Mo who does a mournful version of Cash's Fulsom Prison Blues (Johnnys might be a little celbratory). Mama Tried is about deserved imprisonment and might not be what you are looking for. I think a rapper needs to take that sentiment (mama tried but I fucked up anyway) and make a song out of it.
On the edge of my conciousness is a Texas songwriter's song about crossing the Rio Grande.
There are some really moving Irish folksongs about coming to America. I wish I could remember this one I heard Martin Carthy (or was it John Renbourne) do with some female singer (Maddy Prior?) in concert 25 years ago, but it is another memory just out of reach.
I should also be able to come up with a Jewish immagrant song, but I can't right now.
Check that Smithsonian Folkways site everyone was talking about a few weeks ago. I don't know how easy a subject search is, but there should be lots of stuff and lots of accapelas.
If it were me I would look for songs that say, "I've been kicked around, but I am not down". I would want the overall message to be one of hope in triumph in the faces of struggle.
It took me 2 hours to write this so I am sure other have said some of the same things in the interum.
Dan