Fixed length strings would be very easy to accmmodate as:
EEPROMstringOffset = StringIndex * sizeof(MyString);
If you had to support variable length strings, if you could make a decison about them maximum number of strings you wanted to save up front, you could create an array at the front of the EEPROM that saved the offset to the string which would be the sum of the lengths of the stings stored to date.
Once you know where to write a string, writing it would be easy:
int position;
char *p;
position = EEPROMstringOffset;
p = MyStr;
while(*p){
EEPROM.write(position++,p++);
}
EEPROM.write(position,'\0'); // Save the NULL terminator
NextEEPROMstringOffset = position + 1; // Next String will be stored here