When I look in the gospel accounts, I see the words Jesus speaks when performing miraculous acts are in the form of simple, brief, straight-forward commands--to evil spirits, living things, or elements in nature--or proclamations that the situations had been altered to his will. There are no incantations, no formulaic recitations, no rituals, no preparations, no preparatory meditation, no calling on other powers (except in one case, where Jesus makes it clear it was not for his benefit, but rather for the listeners)--just simple commands given to deal with situations encountered in the course of normal activities, in public areas with witnesses, with no indications that the commands were given in any language other than what would have been common there at the time. He acts with compassion, not for spectacle, even if some would take the spectacular as proof (he resisted the challenge to provide a "sign"). His words are given with the appropriate firmness of an imperative statement, perhaps much like one of us telling a stray dog to "Go home!"
I see that words are a part of the action, but not the essential ingredient. Anybody can say the words. Anybody can give the commands. But enlisted men can't command officers, and slaves can't command their masters. What makes things happen is the authority behind the words, as the sons of Sceva learned (Acts 19).
I see the accounts of the miraculous works of Jesus are meant to testify to the authority of Jesus, whether we believe them to be real events or not--authority over the spiritual realm, over the plant and animal kingdom, and over the forces of nature. Those familiar with the Scriptures would recognize the parallels with the works of Yahweh:
Then he got up and rebuked the winds and the waves, and it was completely calm. Matt. 8:26b
You rule over the surging sea;
when its waves mount up, you still them. Ps. 89:9
He [Yahweh] stilled the storm to a whisper;
the waves of the sea were hushed. Ps. 109:29
And if Jesus had Yahweh's authority over creation, certainly he had authority to forgive sins and teach about how to live.
I don't know the whole significance of speaking the words. Words are how we communicate information to others. It's only meaningful if the communication is accurately understood by the hearer. Do spirits, plants, and inanimate objects need physical communication? I can't see how, but the words do serve as a perceivable link between the source and the object of the power. The words of Jesus expressed his will, so when circumstances were altered, it's clear to those present that Jesus was the initiator of the change--there's no question of who was responsible.
I think this is the same intent of Genesis 1--to show the authority of God. I think this account is about the authority of God over nature which the ancient author wrote about in a way he and others understood, rather than about the process of creation. (It would be interesting to speculate about how this might actually represent physical processes in the formation of the universe. What are words but sound generated by vibrations of the vocal cords. Sounds are waves traveling in a medium. These waves transfer energy. What if the medium was a cloud of hydrogen gas--"without form and void"--in empty space. Wavefronts of certain frequencies propagating in this medium…molecules absorbing energy...well, pure speculation, and maybe no scientific principles we know of to explain it. I'm just suggesting the ancients may have written down something that had an alternative scientific meaning they would never have comprehended. Of course, that would have required some kind of divine influence on the original human source.)