Line break in rotatebox in table?

How about putting the "problematic" header into a \parbox and manually adding \\ (which works inside the box) where necessary?

\documentclass{article}

\usepackage{rotating}

\begin{document} 

\begin{table}
\begin{tabular}{|l|l|l|}
\hline
\rotatebox{90}{Header 1} &
\rotatebox{90}{Header 2} &
\rotatebox{90}{\parbox{4cm}{An awkwardly long \\header that cannot be \\abbreviated in a \\meaningful way}}\\
\hline
Content & Content & Content\\
\hline
\end{tabular}
\end{table}

\end{document}

You can wrap the long header in a \parbox:

\documentclass{article}

\usepackage{rotating}

\begin{document} 

\begin{table}
\begin{tabular}{|l|l|l|}
\hline
\rotatebox{90}{Header 1} &
\rotatebox{90}{Header 2} &
\rotatebox{90}{\parbox{1.5cm}{Long Header Over Several Lines}}\\
\hline
Content & Content & Content\\
\hline
\end{tabular}
\end{table}

\end{document}

You can use \adjustbox{minipage=<width>,rotate=<angle>}{some text\\with line break} from the adjustbox package to create rotated box with the given width which can have manual and automatic line breaks.