English is not my mother language but I will tell you my opinion!
In the phrase 'out of' the word 'out' is an adverb and the word 'of' is a preposition. 'Out' means from inside an object, container, building, or place. We say "The keys must have fallen out of my pocket" or "Charlotte went to the window and looked out". We always say 'out of'!We never say 'out off' because it is wrong!
"Get off the bus" means "Go out of the bus"!When we want to say to someone to go in a bus we say "Get on the bus".In your sentence "Get off the bus" the word 'off' is a preposition.'Off' means 'not on something, or removed from something'. We say "Keep off the grass" or "Someone had taken the mirror off the wall". Do not say 'off of something'! Say 'off something'!We say "Get off the train"!We do not say "Get off of the train" because it is wrong!
In English we can also say "Get out of the bus".This phrase means "Get off the bus".
"Get out of the car" means "Go out of the car".In English we can also say "Get off the car".But this phrase has a different meaning from the phrase "Get out of the car".This phrase means "Go away from the car".We say this phrase to someone who is sitting on the roof of a car or on the bonnet and we want him to go away.
Your sentence "He will have a cake out of the bakery" is correct! Your sentence "He will have a cake off the bakery" is wrong!In English we can also say "He will have a cake from the bakery".
Your sentence "You can get drunk off it" is correct!Your sentence "You can get drunk out of it" is wrong!In English we say "You can get drunk from it" or "You can get drunk on it" or "You can get drunk on beer and whisky"!
Your sentences "This will change the irreparable damaged that has been done to the Gulf of Mexico and the people that live off it" and "This will change the irreparable damaged that has been done to the Gulf of Mexico and the people that live out of it" are wrong! Avoid saying "This will change the irreparable damage that has been done to the Gulf of Mexico and the people that live off it" or "This will change the irreparable damage that has been done to the Gulf of Mexico and the people who make their living from it"! These sentences are correct but their meaning is not clear! It is better to say "This will change the irreparable damage that has been done to the Gulf of Mexico and the people that live off it will be happy" or "This will change the irreparable damage that has been done to the Gulf of Mexico and the people who make their living from it will be happy"! I have changed a little your sentences!Now,the meaning of the sentences is clear!Now,everybody who reads these sentences understands what we want to say!
The word 'damaged' is an adjective.It means 'harmed or spoiled'.We can say "They are selling off damaged goods at reduced prices" or "Both the cars involved in the accident looked badly damaged".
The word 'damage' is a noun. It means 'harm or injury'.We can say "Strong winds had caused serious damage to the roof" or "Recent discoveries about corruption have done serious damage to the company's reputation" or "The doctors were worried that he might have suffered brain damage".
The plural form of the noun 'damage' is 'damages' which means 'money that is paid to someone by a person or organization who has been responsible for causing them some injury or loss'.We can say:"The politician was awarded $50,000 in damages over false allegations made by the newspaper".