I think you can disable DivX logo in its "Decoder Configuration Utility". Go through [Start] > Programs ... etc. In the version I still use (5.2.1) it's on the tab "Quality settings". Perhaps it is similar for "divx setting manager icon" to (not) appear in system tray?
P.S.: I know there have been problems concerning system tray earlier, so could you please let us know if your problem persists or whether you solved it.