Visa is the permission to enter the country. What matters is your status. When is the expiration date on your I-94 (it is likely electronic) or an admission stamp? If it is D/S, then when does your SEVIS record expire? It is indicated on your DS-2019. This determines when your status expires.
You will most likely be allowed to leave with an expired status. When re-entering, the fact that you overstayed makes you ineligible for the VWP.
I would suggest going to Canada and back, as departures to Mexico by land are often not recorded. Upon readmission from Canada or Mexico make sure you clearly state you intend to enter using WVP, and present your ticket back home if requested. Have a backup plan if you are denied admission.
The alternative is changing your status to that of B-1, by filing the change of status paperwork with USCIS I-539. Currently, such requests made in August 2016 are being approved. However, you can stay in the country while petition is pending.
BTW, When re-entering by land, ESTA is not required (although having one will make your entry quicker, as you do not have to pay for and fill out an entry form)
PS. The above does not represent legal advice, and is provided just for everyone's information.