I don't normally check raw log data because my parking company(Namedrive) doesn't normally let me see it unless I email them and ask for it. I did it only once, when I wanted to see from which browser does the traffic come from to my russian IDNs, and it appeared to be Opera. Which is kind of sad actually, because starting from the beginning of this spring Opera discontinued appending ".com" to whatever is written in the URL bar, and so traffic is supposed to decrease, even though I didn't notice much of a decrease yet.

Well, I guess you should look at the origin of traffic first. If the traffic seems organic, then I wouldn't worry that much.
If you see that traffic is highly suspicious, like all coming from one IP, then you should probably somehow block that IP from visiting your page.