I am writing a novel set in the American 1920s with some paranormal elements (none of the characters are human) and I was wondering where I might begin my search with primary sources or at least some sources that aren't a blog post about the best Prohibition era cocktails. I want to know how the ordinary person lived back then to make my story come to life!
The 1920s were not that long ago relatively speaking. Many books published during the 1920s are in the public domain in the United States of America; newspaper archives often provide blow-by-blow of daily life and events; the Library of Congress has a number of online photo collections that show people from the 1920s as they were in all walks of life.
For general goods that were available and their prices, you can often still find Sears & Roebuck catalogues of the period, some of them digitized online. Several prominent writers and politicians have had collections of their letters from the period published, including H. P. Lovecraft's Letters to Rheinhart Kleiner and Letters to Alfred Galpin; Henry Miller's Letters to Emil; Hart Crane's Robber Rocks: Letters and Memories of Hart Crane, 1923-1932; and the first four volumes of The Letters of Ernest Hemingway are only some of the first-hand accounts of the period which are readily available.
While not as reliable on factual matters, there are some fictional works that give a great look at the psychology and sociology of the period, such as Sherwood Anderson's Winesburg, Ohio (1919); for local color there are always the many regional writers of the Federal Writer's Project.
Reading up on the occult and paranormal during this period is also not terribly difficult; I would suggest Lewis Spence' Encyclopedia of Occultism (1925) as a general starting point, then branch off from there in whatever direction catches your interest - Theosophy, Spiritualism, Zora Neale Hurston's explorations of voodoun and rootwork, Aleister Crowley and Thelema, the Society for Psychical Research, etc.