In British football, and Britain in general (I infer this from the novel/film Nil By Mouth), nil is the equivalent of the Yank’s nothing. Referring to the local soccer team, the Union, Mike Jensen writes in today’s Philadelphia Inquirer:
Please don’t refer to the score of a Union game as “one-nil” or “a nil-nil draw.” England may have invented soccer, but it hasn’t won the World Cup in 4 1/2 decades and its national team coach is Italian. The rest of the world has moved on. “One-zip” is just fine, or if announcers want to go with soccer’s actual international language, try “uno-cero” or “cero-cero,” since Spain is now ground zero for the real innovation in the sport.
David Friedman will have to clarify this point, but my impression is that the most commonly heard form is this one (taken from the website of Central Michigan University Chippewas): “Despite a nil-nil draw, Stafford believes his team continued to improve.”
Is it possible that nil and other British football terms will migrate to American sport? Will supporters gathering to cheer their side as they battle on the pitch? At the end of the day, what will be will be.
notoneoffbritishisms.com 
Well, ‘nil’ is hardly restricted to football/soccer in British use. Remember the picture NIL BY MOUTH a few years ago? Once my mother, who like most Brits had little by way of a religion, answered “Nil” to the question “Religion?” on a form she had had to fill in on being admitted to hospital.
In Australia, we would say ‘nil-all draw’.
Just to be different a nil-all draw is called a no-score draw by the football pools to differentiate it from a score draw which has a different value.
This would rarely be used in the UK outside the football score context. Nil by mouth is medical jargon, meaning that a patient is not to eat or drink anything. I can’t think of other common uses of the word.
Nil in football scores is like deuce in tennis scores, anomalous and strictly limited to its specialist field. The medical use is just Latin, like many medical terms, not connected with the football score
“Deuce” is hardly confined to tennis, as witness its role in myriad card games. Not to mention its role as a euphemism for the Devil.