Furthermore I think that it's no problem with WiFi/radio because if I power the 433MHz receiver by an external powersource and not by the Arduino, everything is fine. Only if the ESP and the 433MHz receiver are powered by the same supply (or atleast have linked grounds) the problem occurs.
They should always have linked grounds. It shouldn't work when they don't have linked grounds.
A picture of your setup might enlighten us, too. If you've got long leads for power they can certainly pickup noise.
The last paragraph in this Wikipedia article http://en.wikipedia.org/wiki/Decoupling_capacitor is a good general recommendation:
Since capacitors differ in their high-frequency characteristics (and capacitors with good high-frequency properties are often types with small capacity, while large capacitors usually have worse high-frequency response), decoupling often involves the use of a combination of capacitors. For example in logic circuits, a common arrangement is ~100 nF ceramic per logic IC (multiple ones for complex ICs), combined with electrolytic or tantalum capacitor(s) up to a few hundred μF per board / board section.