I think you're correct that the imperative is the best option for the first two verbs. The second two verbs, though, would be excellent candidates for a hortatory subjunctive. It's also completely permissible to use an adjective as a noun--the only difference is that I would use the masculine, since Darwin's law is about animals, not things.
Here's how I would translate the whole thing:
Multiplicamini, variate, vivant validissimi, et moriantur infirmissimi.
I use multiplicamini because this seems to be an echo of Genesis 1:22: you'll notice that most of the examples in the Lewis & Short entry use the passive for this sense of "be increased."
I also chose vario (instead of muto) because the idea is not only to change, but to change in different ways. Vario is a common word that is mostly synonymous to the English cognate Darwin uses, "vary."