What is [egu-i] mean?
[Egui] is the Japanese slang, often used as a good meaning like [great] among young generation, at the same time it has negative meaning of such as [hard], [tough], [creepy], [weird] and [.
Its origin
Originally it was used to say for describing the taste when people cook. For example the food has too strong scum which stimulate one’s throat and tongue, it used to say [egui]. And later on the meaning has changed to something like [feeling sick] , [strong taste].
However, lately the Japanese comedians started saying [egui] for positive situations on a TV that it has been said that might has influenced the young generation for using it.
When to use it?
We can use for negative as well as positive situation, however as I have mentioned earlier, young people use it for positive situation.
The examples
この景色、美しくてえぐいね。kono keshiki utsukushikute egui ne.
The scenery is so amazing and great!
君のレベルはえぐすぎて、勝てないよ。Kimi no level wa egusugite, katenai yo.
Your level is too great that I can not beat you.
この仕事えぐいわ、疲れた。Kono shigoto egui wa, tukareta.
This work is hard, I’m tired.
ちょっと、彼女のやり方、えぐくない!Chotto, kanojyo no yarikata eguku nai.
Well, her way is cruel isn’t it!

Arigato!
Hope it is informative and interesting to you.