I was sure i was missing something. just a harder to take outpost (when defended) that adds nothing but a spawn point for connected cities? But no: that is all the Awari is.

How is this comparable to all the other districts that gives game long benifits? The chariot is nice but not that fantastic (the myceneans have a more practical unit due to no prequisites).

Can anyone explain me the real strength of this culture?

The Hittites are the weakest faction. Their military bonus is tiny, their unit is good but nothing extraordinary. I much prefer Egyptian chariots or Nubian archers to this, because Egyptian chariots can conquer a city, Hittite chariots not at all.

Besides their chariots require horses and copper, and Wheel technology, so they come rather late compared to the Assyrian Horsemen.

The Awari are good on paper, it's a free fort per region. But compared to the fantastic economic bonuses of the Egyptians or the Harappeans, it's not very useful.

Indeed the Mycenians are much better at all levels: economic bonus, long term bonus, units.

I don't know what it would take to make the Hitites really viable.

It is situational like everything in this game.  If you play on lower difficulty levels you can roll your face across your keyboard and win.  If you bump it up you're going to have to give up your beloved INDUSTRIAL ALL THE TIME strategy and play the map.  I'm currently in a new game where I've started on a map that has 4 enemy surrounding me VERY CLOSE.  I have gone with +Combat Strength across the board to hold my own as everyone stakes territory.  I went with Hittites because I don't want to burn all my population on army and still be able to defend my outposts.  

If you only play "optimal strategies" this game can be very boring. 

In my opinion, not having a proper UD really hampers your influence production as well, since Liberty +2 and +4 on UD is so good compared to the extra vision you get if you go Authoritarian.