Russians drink vodka in several occasions:
1) Someone died (100 g to remember the dead); If it's anniversary of death it is traditional to put full glass of vodka covered with dark bread to the dead person too.
2) Someone got very cold. In that occasion it’s wiser not to take 100 g inside (but you still can do it to warm yourself if you’re already in warm place). Usually we rub frozen parts of the body with vodka, foots for example not to get cold. In the case of some emotional shock someone can offer you to drink glass of vodka at stretch just to calm down and clear your mind. You can use vodka as antiseptic if you have wound and don’t have any other antiseptics.
3) To celebrate some momentous event (advance in rank, for example, or child birth). NikaDimm writes about advance in rank celebration: “Washing the stars (or medal) means celebrating the new rank or the new award. Officer puts stars or medal into the glass, fills the glass with vodka (that's nearly 200 grams) and drinks full glass in one shot. And then he says his new rank and surname and all other officers congratulate him. I don't know if there is a similar tradition for women officers but for men it's a whole ritual fervently observed. If for some reason an officer can't do it immediately he will wear old uniform (one for previous rank) until he has an opportunity to wash his stars. Only after that he puts new stars on his uniform”.
But still vodka was not respectful drink. Poor people drank vodka, cuz it was rather cheap drink compare to others. For example, the cheapest cognac was three times more expensive than vodka. Vodka was bought for big celebrations when many guests were invited, and it was expensive to buy wine for everybody. Common workpeople drank beer after work more frequently than vodka. Wine was for holidays. People in villages made samogon (alky). Some Soviet man from good (probably intellectual) family who was sent to work abroad wouldn’t drink vodka with preference over other drinks. Especially if he have big chose in drinks. Suppose Illya is feeling very dull and depressed. Of cause he can drink vodka, but much more likely it would be cognac, or brandy, or wisky. If he’s nostalgic about his Motherland, well, maybe it’ll be vodka. Still we don’t think that he drank vodka back in the USSR, so why should he drink it to remember his country? So there are two most probable situations, when he will drink vodka – 1) someone died and he’s very upset; 2) he got advance in rank/was medaled and he drinks vodka in order to celebrate it.
Funny thing is that sometimes when you’re abroad it is easier to drink vodka than to explain why you, Russian person, don’t drink it )))
It is important to remember that vodka is drunk at stretch. That’s why we use that 100 g glass (shot glass). You drink it all at stretch and take snack at once. We don’t savor vodka. It’s not cognac to savor it. Actually it’s rather unpleasant drink which can burn your mouth if you keep it there for too long. We don’t put ice in vodka too, but it’s better to drink it cooled. Besides Russians don’t low the degree of drinks. We will not drink beer after vodka for example. Only the rising of degree, just this way))
In the USSR vodka was very masculine drink. It’s even obscene for woman to drink vodka.
I'm not sure, but in canon Illya seems to drink nothing stronger than wine (once it was slivovitsa though). Maybe there were other strong drinks?