The game offers those options passed to it by Windows/DirectX. Usually missing resolution options are a result of the drivers not reporting their capabilities accurately, or of a plain missing monitor driver.

Anyway, you can indeed set the resolution manually as you thought--the file you'll need is as follows:

Vista:
C:\Users\your username\AppData\Local\Ironclad Games\Sins of a Solar Empire\Setting\user.setting

XP:
C:\Documents and Settings\your username\Local Settings\Application Data\Ironclad Games\Sins of a Solar Empire\Setting\user.setting

Please note that some of these directories are hidden by default. To unhide them, go to Control Panel -> Folder Options -> View and set yourself to view hidden files and folders.