pgfplots - barplot with multiple bars on same coordinate, but labelled differently

You can adapt the method from Center nodes near coords in a stacked ybar plot to use nodes near coords for the labels:

\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}

\begin{document}
\makeatletter
\pgfplotsset{
    calculate offset/.code={
        \pgfkeys{/pgf/fpu=true,/pgf/fpu/output format=fixed}
        \pgfmathsetmacro\testmacro{(\pgfplotspointmeta *10^\pgfplots@data@scale@trafo@EXPONENT@y)*\pgfplots@y@veclength)}
        \pgfkeys{/pgf/fpu=false}
    },
    every node near coord/.style={
        /pgfplots/calculate offset,
        yshift=-\testmacro
    },
}
\pgfplotstableread{
0 35569 8842    134984  
1 30428 4689    34077
2 32920 6207    73787   
3 16462 7562    23496   
4 12315 8572    16565   
5 76572 19572   26030   
}\dataset
\begin{tikzpicture}
\begin{axis}[ybar,
        width=15cm,
        height=8cm,
        ymin=0,
        ymax=150000,        
        ylabel={Y-Label},
        xtick=data,
        xticklabels = {
            Category 1,
            Category 2,
            Category 3,
            Category 4,
            Category 5,
            Category 6
        },
        xticklabel style={yshift=-8ex},
        major x tick style = {opacity=0},
        minor x tick num = 1,
        minor tick length=2ex,
        every node near coord/.append style={
                anchor=east,
                rotate=90
        }
        ]
\addplot[draw=black,fill=black!20, nodes near coords=Data 1] table[x index=0,y index=1] \dataset; %Data1
\addplot[draw=black,fill=black!40, nodes near coords=Data 2] table[x index=0,y index=2] \dataset; %Data2
\addplot[draw=black,fill=black!60, nodes near coords=Data 3] table[x index=0,y index=3] \dataset; %Data3
\end{axis}
 \end{tikzpicture}

\end{document}