Does "Dependent" mean and include members of the family who live overseas and do not have a US Social Security Number?

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No.  You generally can't claim a person as a dependent unless that person is a U.S. citizen, a U.S. resident alien, a U.S. national, or a resident of Canada or Mexico. Children are usually citizens or residents of the country of their parents.  Further, in order to claim someone as a dependent on your tax return you have to enter either a social security number (SSN) or Individual Taxpayer Identification Number (ITIN) on your tax return.  Here is IRS Publication 501 for reference.   

You can also check this link for information on applying for a Taxpayer Identification Number (ITIN or SSN).