"I live in an EU country and don't have Earth grounding for my house." That is a common situation in some countries, but is NOT the case in the USA.
For the "EU" style system, imagine a power company transformer somewhere near your house. That transformer steps down a very high AC voltage (1000-5000VAC) to the 220VAC that you expect and routes that lower voltage to one or more customers via a pair of wires. There is no formal (i.e. deliberate) grounding provided; both of the 220VAC wires are ideally floating, not connected anywhere to ground. However, there are at least two causes why touching a 220VAC wire at the same time as earth/ground can produce a shock (or worse).
First case: The transformer itself has capacitance between its high voltage AC input and its low voltage (220VAC) output; this means that AC current can flow through that capacitance from the high voltage primary wires into one or both of the low voltage secondary wires. [All capacitors can pass AC current of some amount, with little being required to shock a person.] The current flows through the capacitance, through the low voltage wire, and through you to earth. Meanwhile...somewhere (perhaps many kms away) there is a connection from the high voltage wires to earth via either another capacitive path or via a direct connection. After shocking you, the current passes through the earth all the way back to the distant ground (either direct or through capacitance) of the high voltage wire...completing the necessary loop for current flow.
Second case: 220VAC is available to your neighbor using the same wires that provide 220VAC for you. However, your neighbor has either deliberately or accidentally made a connection (either direct or via capacitance) between one of his 220VAC wires and earth. That means that the wire your neighbor has NOT made a connection to is now 220VAC relative to earth--it is no longer floating. If you touch the wire your neighbor has not grounded, you will certainly be shocked (or killed).
In reality, both cases (and others) can exist at the same time, complicating the analysis but still shocking you. :)