I am trying to extract the unix timestamp (epoch) from a date string as follows:
var week = $("#week").val();
var timestamp = moment(week).format("X");
You need to tell moment the format of the date string you're trying to parse. I think you're looking for something like this (not tested):
var timestamp = moment("03-Nov-16", "DD-MMM-YY").unix()
See the official docs on date string parsing for more info.