The original meaning of the word literally meant 'to induce awe' i.e. 'to induce admiration or even fear'. If you hear it used in everyday English, it will usually be in the modern sense which means 'amazing', which just goes to show how languages evolve and words' meanings can distort over time. You frequently encounter the original meaning in an historical or religious context.

"Awesome" meaning "extremely good" is a fairly recent usage, and the American Heritage dictionary classifies it as slang. Let me lead up to the slang usage with a number of examples of standard usage. All these examples are correct. 1) The mysterious giant rock formation called Devils Tower filled me with a sense of awe. 2) The only time I've seen the Northern Lights, it evoked a sense of awe and wonder. 3) When the scientists saw the first atomic bomb explosion in 1946, they were awed at its power. 4) The Taj Mahal is a structure of awesome beauty. 5) Pictures cannot convey the awesome destruction caused by the hurricane. 6) People who have been invited to ride in a jet fighter plane with the Thunderbirds say that the power and acceleration of the F-16 is awesome. 7) A Tesla's electric car's acceleration in "insane mode" is awesome. 8) The performance of the New England Patriots (American football team) in the Super Bowl was awesome. 9) Bill was wearing an awesome jacket yesterday.

Yes, to add to what Edward said, typically people using it the word today use it casually for anything they find pleasing. "Awesome party" "They make awesome sandwiches" or even when they don't know what else to say. "I spent the night studying for my exam" - "Awesome!".

Of cause, contradictory. I've just slightly confused the words.

Maybe you are referring to sarcasm? (the use of words that mean the opposite of what you really want to say especially in order to insult someone, to show irritation, or to be funny) In that case it's not about the word "awesome" itself, but the way any word is used in a sarcastic way, e.g. A: "Your car was destroyed" B "Great~! Awesome~! Just what I needed~!"