EVEN THOUGH 
Even though is used to express a fact, something that is real or true.
'Even though' precedes a statement of fact.
It means 'despite/in spite of' the fact.
It is more emphatic or stronger than 'though' or 'although'.

• Even though John is rich, he lives in a small house.
  (John is rich, but despite having money he lives in a small house.)
  
  
• Even though she likes animals, Mary doesn't want a dog.
  (Mary likes animals, but in spite of that she doesn't want a dog.)
  
  
• Even though the building was damaged, business went on as usual.
  (The building was damaged, but despite that business went on as usual.)
  
  
• Even though I washed it several times, I couldn't get rid of the stain.
  (I couldn't get rid of the stain despite washing it several times.)

EVEN IF 
Even if is used in a supposition or hypothesis.
It refers to an imaginary or unreal situation.

• Even if Caroline earned a big salary, she would not buy a fast car.
  (Supposing Caroline earned a big salary. She still wouldn't buy a fast car because she thinks they are too dangerous.)
  
  
• Even if I had time and money, I still wouldn't go on a cruise.
  Supposing I had time and money. I still wouldn't go on a cruise. I have other reasons for not going.)
  
  
• I wouldn't wear that dress even if I got it for nothing!
  (Imagine getting that dress for nothing. I still wouldn't wear it!)
  
  
• Never confide in Linda even if she promises not to tell anyonoe.
  (Linda may make promises but she can't be trusted.(
  
  
• Even if Tom was offered a job in New York, he wouldn't accept it.
  (Supposing Tom was offered a job in New York. He wouldn’t accept it because he doesn't like big cities.)
  
  

Although/even though and despite/in spite of are used to combine or link two contrasting statements.

• Although/even though are followed by a subject and a verb.
  
  Even though is a slightly stronger form of 'although'.
  
  Although and though have the same meaning and are interchangeable in most cases.
  
  
  • Although/even though it was raining, she walked to the station.
  • Although/even though he had enough money, he refused to buy a new car.
  • Although/even though Amy was wearing glasses, she couldn't read the notice.
  Although/even though he disapproved, he said nothing.
  • Although/even though Jack had worked hard, he failed the exam.
    
    
• Despite/in spite of are followed by a noun, a pronoun or a verb ending in -ing.
  (The gerund, a verb ending in -ing, is the 'noun' form of a verb.)
  
  N.B. Despite/in spite of  have the same meaning, but despite is used without 'of'.
  
  
  • Despite/in spite of the rain he walked to the station.
  • He noticed the rain but he walked to the station in spite of it.
  • Despite being wet and tired, he walked to the station.
  • He decided to go sailing despite/in spite of the bad weather conditions.
    

Example:
He had enough money. He refused to buy a new car.

The above two statements can be combined as follows :

• Although/even though he had enough money, he refused to buy a new car.
• Despite/in spite of having enough money he refused to buy a new car.
• He had enough money, but despite/in spite of that he refused to buy a new car.
  

EVEN SO 
‘Even so’ follows a statement of fact.
It means ‘although that is true’ or ‘nevertheless’.

• Our instructor was very strict. Even so, we liked him.
• The weather was cold and wet but even so we enjoyed our trip.
• Her English wasn't very good but even so, she managed to explain the problem.
• His letter was full of mistakes. Even so, the effort he made was appreciated.