At the risk of saying something foolish, I won't attempt to answer the question myself. I understand that all three synchronically more or less equivalent and substitutable, but it would be quite nice to know the traditional usage notes on the abbreviations.
As far as I know, pg. is not an acceptable form, at least in formal writing. The correct forms are p. for a single page, and pp. for a range.
In many cases, actually, you don't need any of them. Quite commonly you'll find references in the form volume:page(s), like 5:204 or 8:99–108 (or, for works of a single volume, something like Blah Blah Blah 108).
The APA style of referencing, which I have most frequently used, requires that p. is used for single page references or citations (Book Title, p. 13) while for multiple pages you must cite it as (pp. 35-40). So p stands for page, pp stands for pages. I have not encountered pg to be used, but I do use it in informal note taking.
Per Strunk and White's Elements of Style, p. is used to denote 1 page, pp. to denote a range of pages. This form of citation is used when you are using brief/in text citations. Otherwise, one would use the citation style for the type of formal paper that you are writing, for example, MLA would be "don't do it wrong" (Author's Last name 45) where the numbers indicate the page number where the quote is found, and the author's full name will be listed (along with other details about the source) in your works cited list.