Dear All,
I am not Indian, but I can share with you my experience, somebody might find it useful, or at least encouraging.
If you are wondering whether you can or not apply for the waiver from outside US, the answer is YES. My J1 expired a couple of years ago, but since I was not interested to extend in US, I never cared about the waiver. Until the end of last year, when for personal reasons I wanted to return to US. During all these years I lived in a third country, other than my home, therefore I am still subject to the 2 years rule.
At the beginning I did not have a clue from where to start the process, nor did I have the money to hire a lawyer. A Native American helped me understand what the DOS requirements are on their web page. Slowly I started to put together the paperwork. You are right, that the No Objection has to be issued by your country's embassy in Washington. Try to find the requested paperwork necessary for your Embassy, on their website. In my case, the Embassy asked for evidence from the Ministry of Education that did not sponsor my internship while I was in the States; a paper from the Finance that I don't have debts in my country and finally a Statement of Reason.
I recommend you, once you gather the documents and send it to the Indian Embassy in DC, keep calling them regularly, until they issue the No Objection and they send it to the DOS.
In order to fill out the online application with the DOS, all you need is the passport and your DS 2019 or the old IAP 66. You submit the form, along with the fees and two self addressed envelopes, which will be used later by the DOS to send you the recommendation. You can write your home address in India, since you are going back, they will mail it to you.
With an expired J1 and application sent outside US and outside my home country, I received the DOS favorable recommendation 2 months ago.
Since then my case has been pending with USCIS for the final approval.
Keep my advice: at any point of this frustrating process, don't give up hope and be persistent, if you know that there were no government funds involved in your internship or J1 program, there's no reason why the No Objection from your Embassy should not be granted and that letter is pretty much decisive in the DOS' recommendation.
Have a lot of faith and keep praying to GOD , things will work out, just remember it's a long exhausting process.
Wadi