Is it possible to suffer from water intoxication drinking about 3 to 4 liters after a heavy meal?

No. Usually seen in psychiatric disorders, water intoxication occurs causing a low sodium level , with generally 15 to 20 liters intake. The kidney can dilute the urine and get rid of water quite well unless it is overwhelmed with that amount. The sudden lowering of sodium can cause serious neurological problems.
Possible, not likely. Individuals with normal kidneys can manage to excrete that kind of water load, although it depends on how quickly it is consumed. If it is "chugged" rapidly, it is possible to overcome the kidneys ability to excrete the excess water, lowering serum sodium and resulting in signs and symptoms of water intoxication, including confusion, delirium and seizures, esp. With big meal holding it in stomach.

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