Well, first off, congrats on your new purchase! Yours is one of the many off-brand machines made in the late teens/early twenties, mostly by furniture companies looking for a quick buck as the main patents for acoustic phonographs (formerly held by Victor, Columbia, and Edison) expired. Most of these were built for their design, and had generic phonograph parts obtained from other companies dumped in.
I did do a quick check on
this, and this was the closest match to "Son-O-Phone":
"215. Sona-Tone -- Sona-Tone Phonograph Inc., 110 West 40th Street, New York City. July 1919."
(warning, massive wall of text alert!)
As for why only two records worked, my guess is that your other records were made in the late '40s/'50s when the material changed from heavy shellac to the modern day vinyl, which is too light for the old acoustic record players. Generally, you should avoid playing 78s made after the mid 1930s on acoustic talking machines due to a change in the shellac composition (pre 1935 78s had an abrasive that wore down the steel needle instead of the record, requiring the needle to be changed every 1-2 plays, and the record would go mostly unharmed), and electrically record 78s tend to be too loud for acoustic machines (with some exceptions, like the Columbia Viva-Tonal and the Victor Orthophonic lines). You can find what year your records were pressed by researching label designs, songs, and some discographies exist for major record labels. I'd also recommend getting the motor restored by
the Victrola Repair Service. As you seem to be an antiques lover, I guess you can handle restoring the finish and replacing the turntable felts and de-rusting the metal parts, but the motor is something best left to someone with experience (the springs can take an eye out, and the ancient grease is yet another problem

). Getting the reproducer rebuilt will definitely help with the sound quality (cracked and dried up reproducer gaskets do not sound pleasant). Plus, the Victrola Repair Service is approved by the Better Business Bureau, so you're not dealing with some scam-artist on the internet who does shoddy repairs at best.
http://victor.library.ucsb.edu/
http://www.majesticrecord.com/labels.htm
Also, pictures please!