I am a physician with J-1 visa and subject to the two-year home residence requirement. After a marriage with an American citizen, do I still need the J1 waiver before I can apply for U.S. Green Card? Also, if I apply for IGA J1 waiver, do I still need to work for 3 years under H1B status? 

A J-1 visa holder who marries an American citizen is still subject to the two-year home residence requirement, and must either obtain a J1 waiver or fulfill the two-year home residence requirement before you are eligible to obtain permanent resident status - U.S. Green Card. 

If an Interested Government Agency (IGA) J1 waiver is obtained, as a physician, you must still work in H-1B status for three years before applying for permanent residence.