Is this grammatically correct: "In terms of whether he will like the gift or not,... ."?
In terms of whether he will like the gift or not, they contradict each other.
or
In terms of whether or not he will like the gift, they contradict each other.

Question

Answer

In spoken English they are both equally correct. In most cases of written English, they are both fine as well. 
In American Enlish, "whether or not" is very common and would sound correct to most people. However, one could argue that the correct sentence would be "whether he likes or whether he does not like". That longer form can be shortened to "whether he likes it or not".

This isn't a formal answer, it may just be a regional usage. To my ear, saying "whether he likes it or not" sounds very forceful. "I'm going to tell that person what I think whether they like it or not."
"Whether or not they like it" sounds a little bit more gentle. "I'm just curious whether or not you've seen him."

Answer

Both are correct. To my ears (British, London) and for written language, definitely the first one. The second one is not wrong but just sounds less elegant. Technically, you don't need "or not" at all because it is implied by "whether".

Answer

Hi - in order to be able to answer your question, I would need to know what "they," refers to?

Who or what 'would contradict each other'?

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