A very common technique in poetry is alliteration: the repetition of initial consonant sounds (for example, "Peter Piper picked a peck of pickled peppers" repeats the "p" sound at the the beginning of most of its words).
"We Shall Overcome" contains many cases of alliteration. For example:
a) "deep in my heart I do believe";
b) "We'll walk...";
c) "wide world."
Another common technique in poetry is imagery: the use of "word-pictures" to represent ideas and emotions. A poet would not usually write, "Relax and enjoy yourself"; rather, he might say, "Kick off your shoes and relax your socks" (see second link below).
Although "We Shall Overcome" is not particularly rich in imagery, it does contain some. Some examples are:
a) "We'll walk hand in hand" (meaning, we'll work and live together);
b) "The whole wide world around."