Incorporated in 1921 as Stromberg-Voisinet, this company's history goes back to 1890, when it was established as the Groeschel Mandolin Company. 

It was one of several musical instrument manufacturers in Chicago during the early part of the twentieth century producing instrument under its own name and OEM instruments for others to brand, (they may have owned the brand name Mayflower but this might have been an OEM brand name too?) I have seen a lot of Stromberg-Voisinet Banjoleles but I have never seen a standard Stromberg-Voisinet Ukulele? They did however make the famous "Aero Uke" in the late 1920's.

Henry "Kay" Kuhrmeyer brought the company in 1928, hired three former Lyon & Healy luthiers and in 1931 The Kay Musical Instrument Company was formed. Kay primarily manufactured "department store" style, inexpensive Guitars, Banjos and Ukuleles, like Penncrest for J C Penny, or Concertone for Montgomery Ward, but also specialized in high end Archtop Guitars. 

Kay also brought out the KeyKord, an early Baritone/Tenor Guitar around the time the company changed its name. This is notable for being one of the first Baritones and because it came with an early autoplayer attached, usually fretless and steel strung. This is most often seen in what is called the "Venetian" Style but some were a more normal figure 8 body shape. Some similar, but bigger models were produced without the autoplayer and with frets as Tenor Guitars, (they also had venetian style Guitars and Mandolins too), it is also the case that some people have removed the autoplayer and added frets at a later date. 

By the mid fifties, the Kay line was centred on electric instruments, (they were one of the original pioneers of electric guitars with models going back to 1928). 

In the 1960's Kay Musical Instruments moved out of Chicago, and in 1965 Kay was sold to Seeburg, a company specializing in jukeboxes. Valco bought Kay from Seeburg in 1967, and during Valco's ownership, Kay's catalogue was simply reprinted with Valco's name at the head, (Valco was also a supplier for Montgomery Wards Airline range which is why these are often attributed to Kay even when they are not). By 1968, Far Eastern competition cause the Kay/Valco company to go out of business. 

In October of 1969 Weiss Musical Instruments bought the Kay name and started using it to rebrand their catalogue. In 1980, a long time employee of Wiess bought the Kay name, and in 1984 the Kay Guitar Company again began manufacturing and importing instruments. This modern Kay incarnation does include Ukuleles but they come from the far east and are of pretty budget standard, (but then some would say weren't they always?)

WMI

Weiss Musical Instrument Co. (or WMI), was a US company founded in 1965 to import Teisco del Rey Guitars, (mainly, but other instruments too). In 1969 they brought the rights to the Kay brand name and started branding their instruments Kay. Prior to this though, they had imported some Ukuleles from Japan themselves and branded them Weiss