Someone Somewhere said:
Can it cause damage? Probably not. However, it could definitely harm/kill you if even the slightest thing goes wrong. Especially if you can feel any tingling when touching them.
Use of devices that requires a ground (not double insulated) without one is illegal in most places.
Actually it feels a strong
tingling when touching them. My landlord won't fix the wiring anytime soon. What can I do as an alternative?
If you can actually feel it, he is required by law
to fix it. "won't fix it" is not an option.
(assuming you are in the US)