I just received a notification that the IRS is thinking of giving us some free money! It is called an Economic Stimulus Payment, and worth $1200 (married filing jointly) and $300 per child.
I checked and it does seem that overseas residents are just as eligible - it's all to do with your Adjusted Gross Income.
We've been notified because we do a 1040 every year. If you don't normally do a 1040 because you don't earn enough, you won't get anything. You need to file a 1040 this year (you are allowed to do this). I think you have to have an AGI of at least $3000 to qualify.
More info from here: IRS