You'll have to settle for a little bit of error for this: In your population data, add a filed called OriginalArea as a double, and calc it to equal the shape area field. Then clip/intersect/identity, whatever your population polygons with your inundation polygons. Add a a field called Percentage in the resulting feature class. Calc it to equal (new) ShapeArea / OriginalArea. Then calc your population field to equal Percentage * Population.
The error in this comes from the fact that population isn't evenly distributed across a census block, block group or track, and the calculation makes that assumption. But when it comes to dam inundation studies, it's close enough. At least it was when I was doing them for State Engineer's office here in Utah some years back....
That should just about do it....