The story so far:
unoconv was installed to me, xvfb-run wasn't there. Hence I followed http://corpocrat.com/2008/08/19/how-to-install-xvfb-x11-server-in-linux-server/. I got the font error described there, so I installed:
yum install xorg-x11-fonts-100dpi xorg-x11-fonts-75dpi xorg-x11-fonts-ISO8859-1-100dpi xorg-x11-fonts-ISO8859-1-75dpi xorg-x11-fonts-ISO8859-14-100dpi xorg-x11-fonts-ISO8859-14-75dpi xorg-x11-fonts-ISO8859-15-100dpi xorg-x11-fonts-ISO8859-15-75dpi xorg-x11-fonts-ISO8859-2-100dpi xorg-x11-fonts-ISO8859-2-75dpi xorg-x11-fonts-ISO8859-9-100dpi xorg-x11-fonts-ISO8859-9-75dpi xorg-x11-fonts-cyrillic xorg-x11-fonts-ethiopic xorg-x11-fonts-misc xorg-x11-fonts-syriac xorg-x11-fonts-truetype
-bash-3.2$ DISPLAY=localhost:1.0 ./unoconv bla.ods
FreeFontPath: FPE "unix/:7100" refcount is 2, should be 1; fixing.
unoconv: UnoException during conversion: URL seems to be an unsupported one.
The provided document cannot be converted to the desired format.
FreeFontPath: FPE "unix/:7100" refcount is 2, should be 1; fixing.
terminate called after throwing an instance of 'std::bad_alloc'
what(): St9bad_alloc
Aborted