I am going to travel to India. I was on H1B visa in the USA and it has now expired. I have a valid Indian passport but the American visa is expired.
If I travel from the USA to India, will I have any problem at the US or Indian airport?
I don't see why the Indian authorities would care about your status in the US, but if they do, explain this (which also explains why you wouldn't have a problem in the US airport):
In the US, a visa is only required as an entry document. Continued stay in the country is not conditioned on the possession of a valid visa.
Sometimes understanding the difference between the visa expiration date and the length of time you have permission to remain in the United States can be confusing. These are very different terms. Also review our “What is a U.S. Visa?” webpage.
I assume you have continued to maintain valid H1B status, in which case you can explain the facts of your employment and so on to anyone who questions it.
Also, the US doesn't have exit immigration controls. They do receive departure information from airlines, but I don't think they would take any action against a departing traveler if they received information indicating an overstay. I suspect they would wait until the next time you tried to enter the country.
This is not even a problem. I went to india and they dont give a damn about your US visa. You are going back home with an indian passport, thats all matters. This is the same about the rumors floating about travelling through any European country with an expired H1B visa. Nobody checked anything when I went through germany.