What about using org-entities for these quotes?
\ldquo{}Hello \lsquo{}World\rsquo{}!\rdquo{}
This is Org mode syntax, not LaTeX.
Adonay:
I wanted to solve this using smart quotes, that is when I write I don't have to worry with anything other than writing, and the light formatting of org-mode is great for that (* for emphasis, / for italics, etc.) While the solution you are proposing is technically correct, it achieves the result, I find it too verbose and distracting from the text.
Actually I solved the problem by upgrading to org-mode 9.1.2 and leaving a space between the inner quote and the enclosing double quote.
Thanks and regards
MartÃn