I'll put a few points forward. I'm really sorry if i'm writing a very long post.

(1) "Like"/"Unlike" is used when you compare nouns/noun phrases. "Like"/"Unlike" CANNOT be used for clauses (A clause has a subject and a verb).

Examples:
Like Cheetahs, Tigers run faster than any other animal. --> RIGHT
Unlike John, David likes to hang around with friends. --> RIGHT

--Like/Unlike must maintain strict parallelism including an article.

Examples:
Like the United States, United Kingdom is keen to build strong relationships with neighboring countries. --> WRONG. Article "the" must precede United Kingdom to maintain parallelism.

Like the United States, the United Kingdom is keen to build strong relationships with neighboring countries. --> RIGHT. Now it's corrected.


-- Like/Unlike accepts modifiers such as "that", "which" etc.
-- Like/Unlike ALSO accepts -ING modifiers (-ING modifiers are not considered verbs), UNLESS a helping verb is attached with the -ING modifier. If a helping verb is attached with the -ING modifier, then "As" must be used for comparison.

Examples:
Like the United States government that promoted a "Go Green" program this summer, the United Kingdom government also promoted the same program this summer. --> RIGHT. Bold parts are only compared. "That" doesn't count in the comparison. It's just a modifier.

My friend is very helpful to others, like my brother working in an orphanage. --> RIGHT. The bolded part is a -ING modifier which could be chopped off.


(2) "As" is used for comparison of clauses OR Prepositional phrases.

-- When you have a prepositional phrase, only "As" must be used. "Like"/"Unlike" CANNOT be used.

Example:
My family lives in Chicago, as in the 20th century. --> RIGHT. Bolded part is a prepositional phrase. Must be paired with "As".

-- When you have a clause for comparison, "As" must be used and NOT "Like/Unlike".

Example:
My teacher teaches Math extremely well in my new school, as does my old teacher. --> RIGHT. Bolded part is a clause ("does" is a verb and "old teacher" is a subject)


(3) "Just as" works very similar to "As". You need to remember an idiom here -- "Just as X, So Y".

(4) As far as i've heard, "Just like" is always wrong in the GMAT. You could eliminate a choice that comes with "Just like".


I hope this helps. Feel free to ask any other question.