A single word to describe someone who is both old and wise [closed]

The closest word I can think of is "sage", which seems to connote someone who is both old and wise.

In certain contexts, it might also be possible to use "patriarch" or "elder", which both imply wisdom or age, but these words add some political connotations that may or may not be desirable.

I'm not sure if there exists a word that includes quirkiness, too. If you don't mind using semi-proper names (in a somewhat more metaphorical sense), you could use "einstein", "oz", or "yoda". These can be probably be used as common nouns, but they may be too strongly tied with the original individuals the words come from.

I am trying to find a word which describes someone who is both old and wise.

The word you are looking for is venerable, which per the OED is:

Commanding veneration or respect by reason of age combined with high personal character and dignity of appearance; having an impressive appearance in virtue of years and personal qualities.

Even if that is not quite exactly what you are looking for, then you should be able to find related terms easily enough.

Regarding the other aspect you asked about, that the advice be odd or difficult to follow, you might start with Delphic. The OED gives one sense for this as "oracular, of the obscure and ambiguous nature of the responses of the Delphic oracle", and provides as a citation the following:

This reads rather like a Delphic response.