Second approach
With the extension Rotate and Scale extension by Ross Moore you can also achieve a similar output. Therefore, load the option \xyoption{rotate} and add the argument [@!<number>] . For further details, see p. 29 of Reference manual
\documentclass[a4paper,12pt]{article}
\usepackage{amssymb}
\usepackage[all,cmtip]{xy}
\xyoption{rotate}
\begin{document}
\def\angle{50}
\xymatrix@!0{
& +[@!\angle]{\alpha} \ar@{-}[rr]\ar@{-}'[d][dd]
& & +[@!\angle]{\beta D} \ar@{-}[dd]
\
\gamma \ar@{-}[ur]\ar@{-}[rr]\ar@{-}[dd]
& & \delta A \ar@{-}[ur]\ar@{-}[dd]
\
& +=[@!\angle]{ax} \ar@{-}'[r][rr]
& & +=[@!\angle]{bx\xi\mu}
\
\Gamma_r(f(x,y)) \ar@{-}[rr]\ar@{-}[ur]
& & \lambda P \ar@{-}[ur]
}
\end{document}

First approach
The answer of David Carlisle to Rotating labels in xypic shows you a possible solution, that is, using for example the \rotatebox command of the graphicx package.
\documentclass[a4paper,12pt]{article}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage[all,cmtip]{xy}
\begin{document}
\def\angle{50}
\xymatrix@!0{
& \rotatebox[origin=c]{\angle}{$\alpha$} \ar@{-}[rr]\ar@{-}'[d][dd]
& & \rotatebox[origin=c]{\angle}{$\beta D$} \ar@{-}[dd]
\
\gamma \ar@{-}[ur]\ar@{-}[rr]\ar@{-}[dd]
& & \delta A \ar@{-}[ur]\ar@{-}[dd]
\
& \rotatebox[origin=c]{\angle}{ax} \ar@{-}'[r][rr]
& & \rotatebox[origin=c]{\angle}{$bx\xi\mu$}
\
\Gamma_r(f(x,y)) \ar@{-}[rr]\ar@{-}[ur]
& & \lambda P \ar@{-}[ur]
}
\end{document}
