Would it be weird if I wrote a poem for the What matters to you, and why? supplement? I wrote something out, but after reading it again, I don’t know if that would be the best plan of action. Should I just scrap what I have and format it to a paragraph form?
It depends on how well it portrays you, I think. The essay is a chance to show yourself. Nobody should judge the content or format of your writing, because no one knows you as well as you do yourself.
Stanford, like all other top schools, appreciates uniqueness and creativity, and I think writing a poem is definetly creative. But it’s better to not to try and be someone that you’re not. In the end, if you feel like the poem suits you well, I’d say yeah, go for it. It’s your application. 
Maybe do both—write the poem, if it expresses you, and then explain it a bit (for people who may not “get” the poem or to add further information).