Example of your .cshtml file:
alert('@Strings.MyString'); //Here you can use your resource string
2) render your strings in variables in a script block in your .cshtml file
and in your .js file treat them like local variables (ignoring the intellisense that's telling your it cannot access the undeclared variable)
var myResourceString= "@Strings.MyString";
<input type="hidden" id="myResourceString" value="@Strings.MyString">
While I'm typing this, I see that the post is a bit old, but it might be useful for someone in the future...