Why does Ohm's law not hold for vacuum cleaners?
It doesn't work for essentially the same reason Newton's laws don't work for resistors (if you apply a force \$F\$ to a resistor of mass \$m\$ which happens to be soldered into a circuit, the resistor will not accelerate with \$a = F/m\$, as the solder joints will hold it back)†. Or, as an even more absurd example, for the same reason Asimov's laws of robotics don't work for celestial bodies.
All laws, certainly all physical laws, only work for a particular, well-defined setting. Ohm's law (in its simplest form, which is what a multimeter assumes) works for idealised resistors. It so happens that a water kettle behaves pretty much like an idealised resistor, and obviously the resistors you use electronic circuits do as well.‡ But a priori, there's absolutely no reason to think a given, unknown component should obey Ohm's law, like there's no reason to assume that Kepler's laws of planetary motion should hold for your water kettle.
Only in a few cases, one finds out that a law which works for some physical object A turns out to also work for a completely different object B. Those incidences are the really exciting moments in physics, like when Einstein proposed that Lorentz invariance, which was first only known as a property of Maxwell's laws of electrodynamics, also holds for massive bodies. That this unwarranted prediction turned out to be true is what makes relativity theory a proper physical theory, as opposed to just some law – like Ohm's law, which is just a description of what, well, resistors do.
†Well, on a level Newton's laws do of course work for resistors: if you apply a force to a that resistor, it will very briefly accelerate until the solder joints apply a counter-force holding it back. All forces together, Newton's law is then again fulfilled. Similarly, even a vacuum cleaner may actually in a generalised sense fulfill Ohm's law, if you consider the motor's inductances as extra (imaginary) impedances/reactances. Those are just not visible to your multimeter, much like the solder joints holding your resistor down aren't visible to the guy who weighed it before you included it in the circuit.
‡Even that is not completely true though: in fact resistance depends on temperature, which is also influenced by the current; and there are more tricky effects like Johnson noise. In a sufficiently pedantic sense, resistors do thus not obey Ohm's law!