We implement part of our game logic with C++ DLLs, some of which provide entry points that are defined with the DLLFUNC statement in the script. I'm looking for documentation that tells what search order Acknex uses to find what it needs for satisfying those DLLFUNC statements. I thought I understood it until a DLL was loaded by surprise, from a location I didn't expect to be searched.

The engine searches first in the DLLs in its plugins folder (normally acknex_plugins), and then in the DLLs explicitely loaded by dll_open(). If you use dll_open(), take care that you don't have a different DLL with the same function names in the plugins folder.

And in the standalone case (no acknex_plugns) wouldn't it search in the executable's folder only?

Unless you gave a different folder through PLUGINS_DIR.