Sort of an educated guess...
...and some surfing...and please remember to take info gleaned on the web with a grain of salt...
Quadraflex may have been the "house brand" for Pacific Stereo, a now defunct retailer...at least according to one site. I found a pair of their 'phones for sale at another for $50US...there was also mention of a quadraphonic reciever at yet another, speaker repair and parts at still another and a TT belt enterprise would seem to have parts for their analog TTs...whether or not these items are in anyway related is anyones guess...given the dearth of info and paucity of references, the "house brand" bit may be the case...I've never heard of 'em and I go back to the days of Heathkits and Lafayette radio and electronics, not that that means much.
Way back when, just about all 'phones were sealed, circumaural models(which by their nature exclude more outside noise) nothing unique in that respect...level and balance controls, even stereo/mono switches were available on some brands and models, I tend to suspect those bells and whistles were more prevalent on lesser brands, but that's debateable...
While closed cups can offer "better" bass response and minimize feedback(required in certain situations), the downside can be one of comfort levels...and the state of the art has improved significantly in open-air design since yours were produced but, if you like them and are satisfied with their sound, what they are or purport to be is really beside the point...
jimHJJ(...enjoy the music...)