While Fn + everything else seems to work, the volume keys aren't doing anything.

Fairly fresh LXDE install, with updates done. (Rather detailed account here.)

Have you installed the EEEPC-ACPI-Utilities package?
It usually fixes most Fn-KEY issues.

Yeah it was already up to date. But now I'm going for the far more radical overhaul as posted by siege (as yet untested in LXDE 3.0, AFAIK), so we'll see if that fixes it.