For an H-1B, you would need to have the equivalent of a 4-year bachelor's degree and this equivalency can be based on foreign education or experience or a combination of the two. The evaluation would need to be done be a certified evaluator.

Do the course completions or certificates from these sites (edx, courseram, etc) count?

and a hell lot of luck because H1B is a lottery system now (which was previously a skill based system)

Why don't you want to stay in India?

A lot of people want to work on more cutting edge problems - at present we don't have companies solving healthcare problems with datascience, or self driving cars, or tesla like companies.

There is also a charm of moving to a more developed economy too.

For many people living in developed countries, moving to a developed economy seems like a good way to travel the world. Though it might be more of a mindset and exposure issue, travelling the world is much easier when one earns in dollars.

It's not like I don't want to stay in India.

@navalsaini has accurately made the point about ability to work on cutting edge problems so that is the main reason.

And I have not even decided yet whether or not to move. I am only checking for options and checking if it is even possible to get visa with no degree.