Why does Ohm's law not work for vacuum cleaners?
The 7.7 ohms you measured is the winding resistance of the motor.  But that is not the only factor that determines its operating current. 

Your vacuum cleaner might draw close to the calculated 30A the instant power is applied, but as soon as the motor starts to rotate, it generates a voltage that is proportional to speed (called back emf) that opposes the applied voltage, decreasing the net voltage available to drive current through the windings.  As the motor speed increases, the current (and therefore the torque produced by the motor) decreases, and the speed settles at the point where the torque produced by the motor matches the torque required to drive the load at that speed.  

Fuses don't blow instantly.  But if you were to lock the motor so it couldn't rotate, that fuse wouldn't last long.