Our hope has diminished.
Nothing wrong here. We use the word diminished with emotions often, particularly when the diminishing emotion is positive. When things are getting better, though, we might not be as likely to say, "Our despair has diminished", instead saying something more like, "Our despair has lifted."
Please diminish your voice.
Definitely not. As individuals, we lower our voices, not diminish them. That said, I think it would be okay to talk about crowd noise diminishing. We walked away from Times Square, and the voices diminished. I wouldn't have any problem with that sentence.
Our sugar supplies have diminished.
You may notice I took the liberty of substituting storage with supplies. Storage doesn't diminish, but supplies can. That said, my revised sentence seems to have a very formal register. I would never say that in my own kitchen, but an executive in a chocolate factory might: "Our sugar supplies are diminished; if the trucks don't get here with a new shipment soon, we'll be forced to shut down the production line."
The flooding has diminished in our area.
This is a tricky one. It seems grammatical, but I don't like it – probably for idiomatic reasons. I think I would say instead, "The flooding has receded in our area", which is a more descriptive word, and one my ears are used to hearing being used with flooding.
Diminished means, "to make or become less," but your question brings up an interesting point: that it can sound very awkward when applied to the wrong thing, such as misery, or flooding, or the volume of our music.