Unstructured Information (also unstructured data)(Wikipedia)
information that either does not have a pre-defined data model or is not organized in a pre-defined manner. Unstructured information is typically text-heavy, but may contain data such as dates, numbers, and facts as well. This results in irregularities and ambiguities that make it difficult to understand using traditional computer programs as compared to data stored in fielded form in databases or annotated (semantically tagged) in documents.
A cursory reading of the Wikipedia article on "full text searching" (redirected from "free-text") appears to show that free text may have a natural language structure to it, but that's not necessary. The term "free text" has such a limited mention in the article (it isn't even defined, but the article assumes the reader knows what it means), that I would avoid it where you want precise understanding of what you want to say.
On the other hand, I have never heard the term "free style" in the context of data and information. Style is more often associated with how information is presented, which is different from the information, per se. (E.g., look into the history of CSS if you want to get an understanding in a computer context.)
If you are talking about the format of the information as it's stored, then I recommend structured and unstructured.
If you are talking about how the information is presented, then style counts, and I suggested something like styled or unstyled. Terms like these, including free-style can work with respect to presentation, as long you make it clear what you mean by it.