1. Do I need to notify the IRS or the state government for tax purposes when I move overseas?

   No, you do not need to notify the Federal IRS or state tax system when you move overseas.

2. Does accepting parsonage as an Ordained Minister lower the person's Social Security and Medicare tax liability?

No, the pastor would still have to pay Social Security and Medicare (15.3% total) on the parsonage as well as on their taxable income.  For most overseas staff if they qualify for the Foreign Earned Income Exclusion, the parsonage does not typically lower their tax liability since the Foreign Earned Income Exclusion exempts them from paying federal income taxes on any earned income under $97,600 (as of 2013).