If I file for an extension for my personal income tax for 2002 (and pay the anticipated tax due by 4/15/2003), can I make deductible IRA contributions for the 2002 tax year after 4/15/2003 (but before I file my final 2002 return)?

No.

Our area is expected to qualify under the Federal Disaster Relief program. We expect that the tax filing deadline will be extended for a number of months.

In that case, can the IRA be funded by the new filing date assigned under the relief program?

I believe the service would consider this an extension (from what i recall of other "disaster areas" in the past), and the April 15th deadline would still stand.