I have been on a J-1 Visa for the past two years. My employer has withheld my Social Security and Medicare during that time. They have refused to give me an explanation of why they are withholding my money and I have filed forms to be refunded by the IRS. My 1040 NR is filed in Texas and this is where I sent my forms for the SSN and Medicare refund. Can you explain to me if my employer can withhold my SSN and Medicare? They are also continuing to withhold my SSN and Medicare this year (I am on a 3 year J-1 visa working as a teacher). My employer also seems to think that I can only be exempt from SSN and Medicare for just two years. Where did they get that? The IRS.gov page says nothing about 2 years! Please advise as it is a lot of money that they have withheld! Did I file at the correct place?

J1 visa for Teachers is exempt from FICA taxes for two years. For many countries, even you don't pay federal income tax for 2-years.
What is your citizenship? Only then we can tell you about the tax treaty.