kytrad,

I know nothing about this song's origin, but I remember it from my childhood in Atlantic City, New Jersey {1950s}. I think it was taught to children in elementary school {ages 4 or 5 to 10 or 11 years old}.

I don't recall any movements that we did to accompany our singing {which further verifies that it was probably taught to us by the school's music teacher}.

The words that I remember are very much as you posted them:

I've been to Harlem. I've been to Dover,
I've traveled this wide world all over.
Over, over, three times over-
Drink what you want to drink, and turn the glasses over.

Sailing east, sailing west,
Sailing o-ver the ocean.
You better watch out. Yeah, you better watch out
or you'll lose your girl
in the ocean.