Including default parameter into \def

Just define \graffito with an optional argument:

\documentclass{article}
\usepackage{lipsum}

\makeatletter
\newcommand{\graffito}[2][0.7em]{%
  \marginpar
    [\graffito@setup{#1}\raggedleft\hspace{0pt}#2]
    {\graffito@setup{#1}\raggedright\hspace{0pt}#2}%
}
\newcommand\graffito@setup[1]{%
   \vspace{#1}%
   \parindent=0pt \lineskip=0pt \lineskiplimit=0pt
   \tolerance=2000 \hyphenpenalty=300 \exhyphenpenalty=300
   \doublehyphendemerits=100000
   \finalhyphendemerits=\doublehyphendemerits
   \itshape\footnotesize
   \leavevmode\color{Black}%
}
\makeatother

\begin{document}

This has a graffito\graffito{This is a standard graffito}
\lipsum[1][1-5]

This has a graffito\graffito[-0.7em]{This is a moved up graffito}
\lipsum[1][1-5]

This has a graffito\graffito[1cm]{This is a moved down graffito}
\lipsum[1][1-5]

\end{document}

Side note: the original code has % after 300 and 100000: they are wrong.

Since you're using LaTeX syntax anyway, you can use the LaTeX command \newcommand to set a default argument with: \newcommand\graffito@setup[1][0.7em]{\vspace{#1}...}. If you want to not use LaTeX syntax for educational purposes, you can do the following:

We need a first macro which checks whether the optional argument follows. For this we use \futurelet (definition made \protected because we need an assignment here):

\protected\def\mycmd{\futurelet\next\mycmd@a}

We need to check whether the next token is a bracket, if it is the next macro reads its argument, else we give it its default.

\def\mycmd@a
  {%
    \ifx[\next
      \afterelsefi{\mycmd@b}%
    \else
      \afterfi{\mycmd@b[0.7em]}%
    \fi
  }

Here I use the macros \afterelsefi and \afterfi for some logic branching. They eat their argument and put it after \fi.

\long\def\afterelsefi#1\else#2\fi{\fi#1}
\long\def\afterfi#1\fi{\fi#1}

Finally the last macro needed for this, this one is the one generating the output:

\long\def\mycmd@b[#1]%
  {%
    Argument was: \texttt{\detokenize{#1}}%
  }

Complete MWE:

\documentclass[]{article}

\makeatletter
\long\def\afterelsefi#1\else#2\fi{\fi#1}
\long\def\afterfi#1\fi{\fi#1}
\protected\def\mycmd{\futurelet\next\mycmd@a}
\def\mycmd@a
  {%
    \ifx[\next
      \afterelsefi{\mycmd@b}%
    \else
      \afterfi{\mycmd@b[0.7em]}%
    \fi
  }
\long\def\mycmd@b[#1]%
  {%
    Argument was: \texttt{\detokenize{#1}}%
  }
\makeatother

\begin{document}
\mycmd

\mycmd[1em]
\end{document}