Having part of a song rhyme while the other part doesn't seems to be an effective strategy (e.g., verse rhymes, chorus doesn't). Also, having internal rhymes and near-rhymes helps satisfy the "need" for rhyming and might help "mask" the absense of rhymes in the expected places.

For example, in Woody's "Deportees" ~ a great example, by the way ~ you have the unconventional rhyme pattern of two consecutive words in the chorus, "be" and "deportee." And in Jerry's chorus to Get Down Home, it may be true that "'Away' and 'around' don't even graze a rhyme," but there are two pretty-good pairs of internal near-rhymes ~ "home/wrong" and "self/else".