Tengu are Mountain Ogres/Demons, typically represented as half human, half crow, with the ability to read minds and great skill in martial arts, especially sword. They were reputed to be rather tempermental, one moment happy and playful, the next moment stealing people to feed them to their chicks/children. Obviously these creatures are mythical.
In Japanese traditions, it is not uncommon to have some kind of mythical, or divine origins to a system. For example, Minamoto Yoshitsune was said to have been taught swordsmanship by Tengu, the founder of Tenshinsho Den Katori Shinto Ryu recieved the techniques and teachings of the Ryu in a dream from the Deity of the Katori Jingu (Shrine), Futsunushi no Kami, and had the scroll in his hands when he awoke, and so on. As Ninja were sometimes represented by three legged crows, the link to divine/unnatural, or supernatural aspects is already present. The crow image then further adds to the connection to Tengu as well.
The reasons for this are found in the Japanese culture, really. The Japanese culture is one that prizes tradition, and conformity (for the most part), so coming along and saying "hey, I came up with a new, revolutionary method of using a sword" can be met with some resistance. The idea of a mythical or divine origin counters that, as the person isn't the one coming up with the revolutionary concepts or ideas, so it gets acceptance a lot easier.
The next thing to realise is that the various Ryu themselves tend to treat these histories as historical truth, regardless of what anyone may believe personally. So if you ask the members of the Katori Shinto Ryu about their origins, they will telll you that it was divinely transmitted to Iizasa Choisai Ienao by the Deity of Katori Jingu, and that divine origin is why their art has survived when so many others haven't, as well as surviving so intact and unchanged for so many centuries. In fact, they will tell you that the name of the Ryu is Shinto Ryu (Divine Way School), located at the Katori Jingu, and Truly and Correctly Transmitted from Heaven (Tenshinsho Den). So the very basic concept of the Ryu's name is that it is the Truly and Correctly Transmitted from Heaven (Tenshinsho Den) Martial Art of the Katori Shrine (Katori), the Shinto Ryu.
With that understanding, you will be hard pressed to find much in the way of academic research supporting or debunking these stories, as they are considered allegorical by outsiders, and unquestioned true history in the Ryu itself. What you may be able to find are the details of the founder of each system (or, at least, the claimed founder, or attributed founder), where they learnt, and so forth. But you really need to be looking at individual systems, rather than just "who taught them?"
EDIT: But, if you are looking for some more academic history books, I'd probably start with Kacem Zoughari's "The Ninja: Ancient Shadow Warriors of Japan", although it is certainly not without it's issues. Oh, and avoid anything from Antony Cummins whatsoever.
