I entered the USA on a Visa Waiver Program (VWP) on 1 July 2012 and stayed until 16 Sep 2012 (78 days). On what date in 2013 will I be able to travel to USA again under VWP?
There are no specific requirements for the period of time until you can re-enter the US after a previous visit on the VWP.
Technically there is nothing that would have stopped you from re-entering the US on the 17th of September, or any date after that.
However entry is always at the discretion of the immigration officials at your point of entry. If they believe that you have or are likely to break any of the conditions of your entry then they can refuse you entry, regardless of your previous status or anything else.
The main issue with re-entering after such a long stay would be that they could believe that you were attempting to reside in the US, and possibly even working - however given that it's been around 5 months since you left on your last trip that would seem unlikely.
I would recommend making sure that you have any possible "proof" of your intentions available just in case (including details of what you did during your last stay, and what you intend to do on this trip) - but presuming that you aren't actually planning to break any of the rules of the VWP program (such as working whilst you are in the US) then I would not expect you to have any issues re-entering.