\documentclass{article}
%
\input{ueur.fd}
\DeclareMathVersion{euler}
\DeclareMathVersion{eulerbold}
\SetSymbolFont{letters}  {euler}{U}{eur} {m}{n}
\SetSymbolFont{letters}  {eulerbold}{U}{eur} {b}{n}
\SetSymbolFont{operators}{eulerbold}{OT1}{cmr} {bx}{n}
\SetSymbolFont{symbols}  {eulerbold}{OMS}{cmsy}{b}{n}
\SetMathAlphabet\mathsf{eulerbold}{OT1}{cmss}{bx}{n}
\SetMathAlphabet\mathit{eulerbold}{OT1}{cmr}{bx}{it}
\makeatletter
\def\eulermath{\@nomath\eulermath
              \mathversion{euler}}
\def\uneulermath{\@nomath\uneulermath
              \mathversion{normal}}
\def\eulerbfmath{\@nomath\eulerbfmath
              \mathversion{eulerbold}}
\def\uneulerbfmath{\@nomath\uneulerbfmath
              \mathversion{normal}}
\newcommand{\bfmath}[1]{\mbox{\boldmath$#1$\unboldmath}}
\newcommand{\eumath}[1]{\mbox{\eulermath$#1$\uneulermath}}
\newcommand{\eubmath}[1]{\mbox{\eulerbfmath$#1$\uneulerbfmath}}
\makeatother
\parindent=0pt
\begin{document}
Here are some greek lowercase letters in the normal font
\[
\alpha\beta_{\gamma}^{\delta\epsilon}-\pi\varpi\times\sigma\varsigma,
\]
 in the bold font
 \[
\bfmath{\alpha\beta_{\gamma}^{\delta\epsilon}-\pi\varpi\times\sigma\varsigma},
\]
in the upright font
\[
\eumath{\alpha\beta_{\gamma}^{\delta\epsilon}-\pi\varpi\times\sigma\varsigma},
\]
and in the bold upright font
\[
\eubmath{\alpha\beta_{\gamma}^{\delta\epsilon}-\pi\varpi\times\sigma\varsigma}.
\]
If you want to use them only in exponents and in suffices, a kludge
is required:
\begin{eqnarray*}
X_{\zeta}^{\eta} &  & X\bfmath{_{\zeta}^{\eta}}\\
X\eumath{_{\zeta}^{\eta}} &  & X\eubmath{_{\zeta}^{\eta}}
\end{eqnarray*}

\end{document}