user1189687 already proposed a solution that I think is better, but since I already begun to write this, here is if you want a plain tex solution :
The point here is to recognize that you are in the first case or in the other.
As @Kurt pointed out, it is trivial to do if you know the format of your input.
But here, apparently you don't.
So what I would do would be :
\makeatletter
\def\@themacro #1.#2\end@themacro{%
\def\@tempyr{#1}%
\def\@temprem{#2}%
}%
%
\def\themacro #1 {%
\let\day\relax%
\let\month\relax%
\let\year\relax%
\let\@tempyr\relax%
\let\@temprem\relax%
\@themacro#1.\relax\end@themacro% get day or year
\if\relax\@temprem\relax%
\if\relax\@tempyr\relax%
\GenericError{}{Wrong date format}{}{}% Manage the error
\else%
\edef\year{\expandafter\noexpand\@tempyr}%
\fi%
\else%
\edef\day{\expandafter\noexpand\@tempyr}%
\expandafter\@themacro\@temprem\end@themacro% get month
\if\relax\@temprem\relax%
\GenericError{}{Wrong date format}{}{}% Manage the Error
\else%
\edef\month{\expandafter\noexpand\@tempyr}%
\expandafter\@themacro\@temprem\end@themacro% get year
\if\relax\@temprem\relax%
\edef\year{\expandafter\noexpand\@tempyr}%
\else%
\GenericError{}{Wrong date format}{}{}% Manage the Error
\fi%
\fi%
\fi%
}%
\makeatother%
The advantage of this solution is that you detect incorect syntax and can have a fallback or throw an error, as you wish.
Oh, I almost forgot ... You of course get the year as the replacement text of \year.
In case they exist, you also can get \day and \month.