I don't know which country you're in, so I will go with French rules... which shouldn't be different from your own, since they're pretty much common sense.
First, assume the oven and/or dishwasher are live and do not touch them.
- The sink and pipes should be earthed.
The sink can either be earthed with an explicit wire (mandated by law on new installations, since plumbing often uses plastic pipes now), or it could be earthed through metallic pipes, or not at all.
Recent law mandates all metallic surfaces to be earthed (this is useful if someone drops a powered kitchen mixer into a stainless sink full of water, for example) except of course metallic enclosure of double insulation appliances.
If you have copper pipes and they are not earthed, then any fault in your boiler or other electric appliance which is connected to the pipes can make the pipes go live, which is bad for your health if you're taking a shower or handling water.... or you touch a metal shower faucet, which would be the worst case.
Non-earthed copper pipes mean any faulty appliance/boiler where wires come loose and touch the pipes anywhere (even somewhere else in the entire appartment complex if all the pipes are metal) will kill you dead when you turn the shower faucet, it is no joke.
Locate a mains outlet with a earth pin, and test continuity of earth between this earth pin and your sink, then copper pipes. The tester should ring.
Now, let's check the rest...
Turn off your main circuit breaker and test continuity of earth between a earth pin in a socket and the metallic chassis of your oven and dishwasher.
The tester should beep in all cases.
If it does not, one of the appliances is faulty.
Now, unplug the faulty one, and flip the main circuit breaker back on to have some light.
If the electric installation is old or wasn't done by pros, some sockets could have missing earths (I saw this happen) or even worse, the entire appartment's earth could be connected to nothing at all. If you are paranoid, you can test all earth pins in all sockets... and ask the electrician to check in your main electrical panel that the earth actually goes somewhere...
Oops, I saw you have "no earth" ?
Where are you located? That's illegal here and pretty much everywhere else...
If you don't have earth in your flat, then it is deadly to use any Class-1 appliance (those which need a earthed socket). Which means pretty much everything. Those appliances have a earthed chassis. So when some water leaks into your dishwasher and short circuits between the wires and the chassis, current goes into earth and trips the RCD breaker. Without earth/earth, current goes into you when you touch it.