I am a U.S. citizen supporting my aging sister and husband abroad. Do I get any tax relief?

They would need social security numbers and you would need to provide proof you pay more than half their expenses and that they are not the dependent of anyone else or on welfare. See IRS Publication 501.

I suggest you contact an Accountant.... your sister and husband probably would need a U.S. social security number, and might have to spend half the year living in the U.S.

Probably not in a foreign country. See IRS.gov