I've read that sten guns could start to fire uncontrollably if bumped or treated with little care and that British soldiers started to use this at their advantage to clean buildings by tossing fully loaded stens through windows to scare German soldiers, how true is this?

While it is possible for an improperly handled STEN to go off, it would only likely fire one cartridge if dropped in this case.

In auto-loading firearms, timing is absolutely critical. Cartridge cases cannot support the full pressure of firing. So if you try to pull the empty case out of the chamber while the bullet is still in the barrel, the pressure is so great that you will tear or rupture the case, leading to malfunctions or injury to the shooter. Therefore designers have to design some sort of delaying mechanism to ensure safe and reliable extraction.

The way the STEN works, as well as most similar submachine guns of the time, was through the use of a open bolt blowback system. Blowback basically means that the pressure of the cartridge is resisted by the inertia of the bolt and the spring pressure pushing forward on the back of the cartridge. This bit of resistance gives the bullet enough time to leave the barrel, pressure to drop to safe levels, and the case is safely extracted. Open bolt means that the bolt held to the rear under spring pressure, and when the trigger is pressed the bolt is released, it travels forward, strips a cartridge off the magazine, and as soon as the cartridge enters the chamber it fires. Then the gun cycles back and either picks up a cartridge and fires again if the trigger is still pressed, or if the triggt is released it gets caught by the scear and the gun stops firing.

The doctrine of a lot of militaries was to carry their submachine guns with a magazine inserted and the bolt closed on an empty chamber. This was a safe way to carry the gun in that it prevented the soldier from accidentally firing the gun, and he'd have to make the conceous effort to pull the bolt to the rear before he would be ready to shoot. However, if the gun was dropped vertically with sufficient height, when the butt of the gun would strike the ground, the inertia of the bolt could make it travel far enough back to strip a cartridge off the magazine, but not far enough back to catch the scear and prevent it from firing. Then gun then fires that first cartridge, but since no one is holding the trigger the gun locks open.

Most militaries would include some sort of lock to prevent this from happening. For example the Soviet PPSh 41 has a safety that, when the bolt is closed, can be pushed to the left and locks the bolt forward. When a Soviet soldier would go to ready his weapon, he would have to pull the safety to the right, then charge the gun. However, including that safety added to the cost of the STEN, and the British decided against and accepted the slight safety hazard in order to maximize their industrial output. Remember that at Dunkirk, the British forces lost a huge amount of hardware and were desperate for small arms.

As far as soldiers using a STEN like a grenade, I've never seen a documented case of something like that happening. There are things called runaway machine guns where a mechanical failure causes the gun to fire uncontrollably, so maybe there is a case where soldiers had or created a gun that would fail in this way and used it in combat, but I find it to be a highly unlikely that it actually did.