The weirdest machine that I can think of is probably this twin fan Graybar, which has a fan on either side of the motor and the motor being in the middle of the air path.

The Air-Way DirtMaster is also a pretty unusual machine, being one of only two vacuums I know of to use a belt-driven fan and the only vacuum with dual belt-driven fans, not to mention the fact that the fan case is also the handle pivot. However, I am a bit desensitized to its weirdness since I own one.
This prototype Kirby with the Sani-Emptor built into the body of the machine itself is also pretty strange. I believe the whole bottom half hinges down when the latch on the back is opened.

In terms of stuff that never got made, it's hard to be more deranged than this design that has two nozzles, one on the front and one on the back, both powered by a single motor in the middle. I don't really understand what kind of advantage this would provide. I guess it's meant to clean twice as much in one stroke, but seems too bulky to really work well.
The other patent design that rivals it is this Air-Way with two suction motors in tandem.
I recall seeing some sort of early vacuum that I believe has two large fans on either side of the motor, but I can't remember what it is called off the top of my head.