1. He never wants to work.
2. He wants to never work.
3. He wants never to work.
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Can we use all the expressions?
In #2, 'never' is put before 'work'. Is it a split infinitive? Can we use this way?
No, only #1 has correct word order.
In 2, "never" splits the infinitive. =(
#3 is just plain awkward.
http://grammar.ccc.commnet.edu/grammar/adverbs.htm
Scroll quite a way down and read about order of adverbs in sentences.
All three expressions are grammatically correct and convey similar meanings, but they have slightly different nuances.
In #1, "He never wants to work," the word "never" is placed before the verb "wants." This indicates that the person has a consistent lack of desire or motivation to work.
In #2, "He wants to never work," the word "never" is inserted between the infinitive marker "to" and the verb "work." This is an example of a split infinitive. Split infinitives occur when an adverb (in this case, "never") is placed between the "to" and the base form of the verb. While the use of split infinitives was once considered incorrect in formal English grammar, they are now more widely accepted and deemed grammatically valid in modern usage.
In #3, "He wants never to work," the word "never" is placed before the infinitive marker "to." This structure emphasizes the person's preference or intention to avoid working entirely.
So, to answer your question, all of the expressions are correct grammatically. Whether to use one over the other depends on the intended emphasis and personal preference of the speaker or writer.