The speaker's similes capture the storm's strange power, its deceptions, and its contradictions.
The first harbinger of the storm is a wind that sounds "like Rain"—at least, until it "curve[s]." This evocative simile will feel just right to anyone who's heard a wind moving across a field, then falling off or changing direction.
Such a wind at first sounds like raindrops; as the speaker puts it, it "walk[s] as wet as any Wave," an odd little moment of personification that suggests waves and rains alike plant wet footprints as they go. But in fact the wind "swe[eps] as dry as sand." Besides presenting a surprising contrast with the wind's watery sounds, this simile captures the sense that the wind sounds like millions of little movements happening at once—whether it's the fall of raindrops or the whisk of sand grains.
This tricksy wind moves away, and a new sound intervenes: "a coming as of Hosts." The arrival of the actual rain, in other words, sounds less like rain and more like an advancing army. At first, this martial rainstorm seems oddly friendly: that vast army just tops up wells and "warble[s] in the road" like a playful child. At last, though, it fulfills its dangerous promise and "let[s] the Floods abroad," washing out the whole landscape.
When the rainstorm departs, it goes "like Elijah"—that is, like the biblical prophet said to have ascended to heaven in a fiery chariot carried on a whirlwind. That closing simile suggests that this rainstorm, like a prophet, came to shake things up, to leave the world changed in its wake.