Hey thanks Mitch. I have done a lot of online research on these and the sister company Bronson. This is what I found. They sold "lessons" door to door like vacuum cleaners.

I can see it now "oh little Johnny how would you like to take some guitar lessons, now wouldn't that be fun. Mom, just sign here for lessons and we will provide little Johnny with a guitar"
Oahu nor Bronson ever made a guitar. Harmony, Kay, Valco possibly Regal and Rickenbacker for the electric lap steels. I dug this up somewhere.
"Old Oahu guitars are pretty common. It may be hard to believe, but Hawaiian guitar (acoustic guitars played lap-style with a steel slide) was popular in the 30's and 40's. There were a number of Hawaiian guitar schools at the time. Oahu Publishing was one of the largest. They published sheet music and sold guitars in addition to giving lessons. At its peak it had over 1200 schools. They finally went out of business in 1985. It's estimated that they had 200,000 students over the years.
Often people would sign up for lessons in which a guitar was supplied. At the end of the series of lessons they would get to keep the guitar. Many guitars were inexpensively constructed with laminated woods and simulated wood grain finishes, although yours might be made from solid wood."
Hey Frank, if what you said were true mine would have been made from cardboard.
There is just something about these Oahu's that intrigues the hell out of me. They are like Pringles, you can't have just one. The nice thing is they are affordable. hehehe Next on the list is a Bronson.
"I shall pass through this world but once, any good therefore that I can do or any kindness that I can show to any human being, let me do it now. Let me not deter or neglect it, for I shall not pass this way again" Stephen Grellet