Every one on J1 is exempt from residency for 2-years; and students on J1 for 5-years. During exempt period you don't pay FICA (social security and Medicare taxes).
Read about nonresident filing: :
Your U.S. Tax Return: U.S. Tax Filing Requirements for Non-Residents
For many countries as per tax treaty for researchers the income is not subject to federal tax for 2 years or even more. What is your citizenship?
Yes, you need to amend your tax returns for 2005 and 2006. For 2007 you may be resident but it depends upon your citizenship and your classification: intern, student, researcher...