The base of the bottle bears the mark of Glass Containers Corp. of Fullerton, CA. according to the book, "Glass Makers and Their Marks" by Toulouse. The author states that this particular mark was used after 1945.
Yes, it is an oddball shape. You might browse through the photos of Owens-Illinois which may have a similar shape pictured and sometimes the catalogs suggest the bottle shape's use. You will find a link in this forum somewhere - probably search on the word "catalog"