I assume you're referring to the earliest writers of the region, which takes us clear back to Jamestown and Plymouth. If that's so, the writers were members of those settlements and their writings were journals and other personal reflections. Their common literary style, then, is personal writing to record their histories.
William Bradford's Of Plymouth Plantation is a journal of both the historical and spiritual journey of the settlers of Plymouth. It is clearly written with the intent for others to read it, so it is a personal journal intended for a much larger audience (though I'm confident he had no idea just how large that audience would come to be).
John Smith's General History of Virginia is also a journal, though it was clearly intended to make himself look good. He writes in an affected third person style, so the journal reads less personally (and so he can enhance his own reputation) and more like a general narrative. This journal was reworked for years before publication, so its strict historic perspective has been skewed.
Other writers of the day, such as Anne Bradstreet and Edward Taylor, wrote more spiritual poetry which also contained glimpses into early new England life.
All of them (poets excepted) wrote in the English of the day, which we find difficult to read in the original (think King James Bible, magnified). Their styles, however, were fairly plain and readable by their standards. These were not literary writers; these were historians who chose to write, and they did so in their own styles.
The overall literary style, then, was personal reflection and historical recording. In truth, none of the writing of that time period is particularly artful--they were too busy trying first to survive and then thrive to have much time for anything more literary.
Hope this helps.