The normal copyright laws apply. Old works don't have issues about reuse/republication, but should be cited to the author to avoid charges of plagiarism. Newer works need to observe that "complete" works can't normally be copied without permission. A poem, even if short, is a complete work.
Quotations are probably fine if cited to the original speaker, but these are seldom enough to be considered "complete works" even if new. But over quoting from a speech might bring you problems.
And note that it doesn't matter whether you gain revenue from a work that cites a poem or whatever. For copyright purposes, the issue is whether you are likely to reduce the value to the originator or not. So, short excerpts are normally fine, but at some point you cross a line making it unnecessary for someone interested to go to the original. IANAL, but something like that, anyway. It is a civil matter to be judged in a lawsuit if a copyright holder chooses to bring it.
Note that plagiarism is not the same as copyright infringement. You avoid plagiarism by citation and you don't need to use any form of copying to commit it. Plagiarism is about ideas. Copyright is more complicated and is governed by law. But copyright eventually expires letting you "copy" the words (or sounds or ...). But citation is still needed even if not always to a specific source.
And note that even public domain works should be cited to the originator.
And finally, plagiarism is a social construct, not a legal one. You can be accused of it and suffer the consequences even though you break no laws. The clear implication is that, in any doubtful/edge cases, you cite. Over citation causes no harm.