Looking for a style guideline to put many references in a table

The Chicago Manual of Style (16. ed.) treats table notes in section 3.77. You already follow the guidelines by not using numeral superscripts to prevent ambiguity with exponents. You're also already using the set of symbols proposed by the CMS, except the pound symbol (#). (The footmisc package's LaTeX standard set uses the paragraph symbol (¶) instead of the pound and inserts it before the parallels at position 5).

The CMS's recommended order of occurence is shown in the table below. Should more symbols be needed, doubling and tripling them is recommended. The example table also shows a way to arrange the notes directly below the table by using the threeparttable package. This arrangement complies with the CMS.

Instead of doubling or tripling elements of a set of only six symbols, you might however rather consider using letters, or possibly greek letters. The CMS states that "letters are generally preferred", and should you indeed have really many notes, using a larger alphabet of symbols could make a table a lot more readable.

\documentclass{article}
\usepackage{booktabs}
\usepackage{threeparttable}
\begin{document}
\centering
\begin{threeparttable}
    \begin{tabular}{llll}
        a & b & c & extra width \\\toprule
        1\tnote{*} & 2\tnote{\textdagger} & 3\tnote{\textdaggerdbl} & \\
        4\tnote{\S} & 5\tnote{$\|$}& 6\tnote{\#} & \\\bottomrule
    \end{tabular}
    \begin{tablenotes}
        \footnotesize
        \item[*] Symbol 1
        \item[\textdagger] Symbol 1 
        \item[\textdaggerdbl] Symbol 1
        \item[\S] Symbol 1  
        \item[$\|$] Symbol 1
        \item[$\!$\#] Symbol 1          
    \end{tablenotes}
\end{threeparttable}

\end{document}

Use [para] to write your table note as paragraph

\documentclass{article}
\usepackage{booktabs}
\usepackage{threeparttable}
\begin{document}
\centering
\begin{threeparttable}
    \begin{tabular}{llll}
        a & b & c & extra width & entry1 & entry2 \\\toprule
        1\tnote{*} & 2\tnote{\textdagger} & 3\tnote{\textdaggerdbl} & \\
        4\tnote{\S} & 5\tnote{$\|$}& 6\tnote{\#} & \\\bottomrule
    \end{tabular}
    \begin{tablenotes}[para]
        \footnotesize
        \item[*] Symbol 1
        \item[\textdagger] Symbol 1 
        \item[\textdaggerdbl] Symbol 1
        \item[\S] Symbol 1  
        \item[$\|$] Symbol 1
        \item[$\!$\#] Symbol 1          
    \end{tablenotes}
\end{threeparttable}

\end{document}