When walking in
Well, if the curse is suppressed (by being in antimagic in this case), you become young again. Thus you wouldn't have the age penalties or bonuses.
If you were to be actually old, any magical ability to get rid aging penalties would also be suppressed. So that supernatural ability that grants immunity to aging would not work in antimagic anyway.
When walking out again
The moment you leave, both effects will start working again. Thus you'd be old again due to the curse, and you'd ignore the penalties due to the immunity to aging. This is assuming the duration of those effects hasn't expired (and I'm assuming that they're both permanent, so this shouldn't be a problem). Just like they would work if you never entered the antimagic field.
An antimagic field suppresses any spell or magical effect used within, brought into, or cast into the area, but does not dispel it. Time spent within an antimagic field counts against the suppressed spell’s duration.