Folk songs are about the context as much as the text.
Bruce Jackson writes in the introduction to his book Wake Up Dead Man: Hard Labor and Southern Blues:
There is an important difference in our approach to art song and folk song. Art song requires that we perceive the nature of the art involved; folk song requires not only perception of the art but also the generating or supporting musical social, and historical contexts. Folk song is not simply textual, but con-textual: it does not exist—save for historians and scholars—on pages in books, or even on shiny black discs. It exists in a specific place at a specific time, it is sung by specific people for whom it has specific meanings and functions.
We can't now determine what the original context of the song was nor who wrote the Samson verse. But we do know that it existed in one or more of the places that African music thrived in America: work songs, church worship, and minstrel shows. The most obvious context is Christian and we know the Fisk Jubilee Singers (who avoided vaudeville music) used the song on tour and recorded it in 1911.
Meanwhile, Bruce Jackson also noted that two versions of the song were used by convicts in the Texas prison system. One version repeats the basic refrain and inserts various non-Biblical people into the role of witness: family, fellow-prisoners, guards, even visitors. In this context, the message is clear from a single line:
Anybody can be a witness ...
The other version is an adaptation of the spiritual. Jackson, analyzing the final stanza about a man who caused a stir at church (perhaps a one-man ring shout?):
All the previous stanzas are about situations in which God was involved in people's activities; this stanza suggests that the use of messengers and agents might continue.
The purpose of the song in worship.
As a work song, the purpose is to get by: make a hard day's work go a little lighter and a little more pleasant. But in the context of the church, it must have been something different. Part of the purpose might have been entertainment: the Samson verse fits the bill perfectly. But the other purpose, judging from the other stanza, must have been to remind the congregation of the Biblical stories. Since I wrote the question, I've seen verses about Moses, Ezekiel, Isaiah and Jonah which pick significant moments in their lives to put in verse. One can imagine these verses being passed from one congregation to another (and even back and forth from church to work) and thriving or dying depending on how well they were remembered.
Many of the verses show men sustained by God in hard times. Power to overcome human authority seems to comes from God Himself. Remember that the church was one of the few places a slave could be free to express himself without fear of reprisal—as long as he didn't speak rebellion against his master. So the songs seem to be coded to communicate that God can (and might very well) free people from bondage without saying it outright.
Samson empowered by God; Samson defeated by trickery.
On the one hand, God's hand was clearly on Samson during his time as judge since he was able to easily defeat the Philistines with his strength. But he also used trickery, which was his downfall in the end. When Delilah removed his hair and he became a normal man, it was as much a witness to what God had done as Methuselah living a long life. The song calls it's hearers to be witnesses to the Lord, but it assumes the audience is as powerless as Samson shorn. By implication, God might very well empower someone to become a witness by becoming strong enough to shake off the bonds of slavery and oppression.