I will not explain “but”, because I imagine you know how to use that word correctly. “Nevertheless” means “despite what has just been said or referred to”: “I knew a lot about the subject already, but her talk was interesting nevertheless.” “The building is guarded constantly, but robberies occur nevertheless.” “I had lost a lot of money in the poker game; nevertheless, I decided to continue playing.” “Whereas” is used to make a statement that describes that there is a contrast or difference between the things mentioned: “He must be about 60, whereas his wife looks about 30.” “You eat a huge plate of food for lunch, whereas I have just a sandwich.” “He has brown eyes whereas his children have green eyes.” Replacing “whereas” with “but” in the above sentences wouldn’t change the meaning in my opinion. But replacing “but” with “whereas” in the following sentences would be wrong: “Call me old-fashioned, but I like handwritten letters.” “Everyone in the office complains that he smells awful, but nobody dares mention it to him.” I hope this helps a little.

nevertheless is formal word for "but" whereas means when, while, considering the fact that..., although