Is it grammatically correct to say: If I were you . . . or If it were
me . . .I know this is standard in colloquial English but I have never
understood how it can be grammatically correct - shouldn't the word
"were" be used in conjunction with a plural?

The use of "were" in such a case is an instance of the subjunctive
mood, which is less prevalent in English than in many other languages.

http://en.wikipedia.org/wiki/Subjunctive#The_subjunctive_in_English

and possibles v. hypotheticals
http://www.english.vt.edu/~IDLE/GYM2/workout4/w4.stretch7.html

It's a subjunctive, used "when the content of the clause is being,
doubted, supposed, feared true etc" (to quote Collins Dictionary). For
example, in the phrase "If I were a rich man", the verb "were" is the
subjunctive. It's necessary because the speaker is not rich but wishes
to talk about the hypothetical possibility of being rich, however
unlikely that may be.