"Grandmaster of the catchy tune" suggests Woody made them himself. He never made tunes up, he grabbed hold of the ones he needed and used them. Like a craftsman who spots the right bit of junk or wood lying around, and makes something new out of it.
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As people have said, songs can help people come together and stand together and work together, and it's that kind of thing that gets results. The songs help a little, sometimes they can help a lot maybe. But they are one step in a long journey.

Good songs which can do that can be funny, they can be serious. The one thing they can't be is earnest.