What is the correct way to translate variable_get string values entered in admin input fields?
You should use the Variable translation module, part of Internationalization.


Enable the Variable translation module included with the Internationalization package
Go to Administration > Configuration > Regional and language > Multilingual settings
Click on the Variables tab
Select the variables that will be multilingual
Click Save configuration button


Then, you'll be able to select language for which you are configuring your variable:



Advice taken from this community documentation.