A search of google books found An Universal Etymological English Dictionary, written in 1737 (there are earlier versions but they are not available on google). No mention of Grog, although the dictionary seems pretty comprehensive. There is a mention of Grog'ram (apparently gross grain), a type of fabric. http://books.google.com/books?id=VuYIAA ... og&f=false
There is also a mention of Punch, "a Composition made of Brandy, Lemons, Water, Sugar, et. cet. for common drinking." http://books.google.com/books?id=VuYIAA ... ch&f=false
That to me is pretty convincing that Grog was not a term in common use in 1737. More evidence that we need to have punch at an event at some point, as if we needed it. Punch was a common sailors drink, much in evidence in Johnson's history and other period sources.
Wow, the more I search this dictionary, the more I find! I have often used the period term "Punk" for a prostitute, but it has a nuance and etymology I did not realize. From the dictionary, it derives from "[. . . a Leather Wallet, q.d. an old shriveled Whore, like a Piece of shriveled Leather] an ugly ill-favor'd Strumpet." Wow, I didn't realize how insulting I was being. Will have to use it more!
Interesting entries on sword, han'ger, etc. No mention of Cutlass or its many variants that I can find, but many nautical terms.
Other base woman terms - Giglet, Jade, Wench, Crack, Trull, Strumpet, Que'an (also barren cow), Drab, Slut, Overswicht, Mort, Doxy, Miswoman, Harlot (proud whore) Cuckquean, Cal'let, Bulk'er, Bona-Roba (Spanish), Baggage (soldiers camp-whore). Wow, that is a lot of whore names. Some new ones on me! Comprehensive dictionary for the important stuff!