I am researcher from India. I am in J1 visa. First 2 years I had tax exempt. Now my salary is ~2166 USD/MONTH. I am in 3rd year. Starting this year, I have been taxed every month ~537USD ( with hold). I want to know that how much I can get refund next If I file the tax return. I am single. I am a post doc. researcher in University. Whether I will have tax exempt under "doing non-profit research would be completely tax exempt". Thanks for the answers.

The tax treaty between U.S. and India.
"An individual is exempt from U.S. tax on income received for teaching or research if he or she:
• Is a resident of India immediately before visiting the United States, and
• Is in the United States to teach or engage in research at an accredited university or other recognized educational institution the United States for a period not longer than 2 years.
If the individual's visit to the United States exceeds 2 years, the exemption is lost for the entire visit."

You are in the 3rd year. You are no longer exempt. You will file resident tax return and must pay SS tax, Medicare Tax and Income Taxes.
Also as per tax treaty, you will pay income tax for previous two years also. You will not pay SS tax and Medicare tax.

All what MukatA says is true.

To be clear, you need to file tax returns for the first two years you claimed exempt status to pay those taxes retroactively.

If you filed tax returns for those years and claimed exempt status (and therefore paid NO taxes), you must amend them using Form 1040X and attaching properly-prepared Forms 1040NR-EZ. Expect to pay the tax plus interest (required by law); the IRS MAY waive any late-payment penalties, but that is NOT guaranteed.