When you mentioned this, I remembered that I had once a bicycle that had everything wrong with it.
It was a ГAЗ ШКОЛЬНУК (GAZ Szkolnik), made in the USSR in the GAZ factory in Gorky, mostly known for producing off-road military vehicles such as models 64, 69 and popular full sized cars like the M-20 Победа (Victory), it's succesor "Волга" (Volga), and small trucks like Газель (Gazelle). This bike had 20" wheels, that didn't fit any 20" tires & tubes, headset smaller than 1", smaller axles than normal, even the BB was in a different size than normal, and the rear hub with freewheel & coaster brake was half smaller than normal. Even all the wrench sizes were different than normal.