Yup, "like" can be used as a conjunction. (Check out dictionary.com, the seventh and last definition of 'like.') And that's the sense in which it's being used in the examples we're talking about. ("Like" can be a verb, as in "He likes fish." It can also be a preposition, a noun, an adverb, or an adjective, depending upon how it's used in a sentence.)

Informal, common usage is "I'm not like him," but put that implicit verb back in there--"I'm not like him is"--and suddenly you can see how it sounds weird. It really does expand into two independent clauses, "I am" and "He is."

Your final example is indeed incorrect, but that's because in that sentence "he and I" is the indirect object of "to give."

I'm going to go look this up in some offline sources this weekend to see if the confirm it, though.