I haven't used MapObjects since 2.0 was released, so all I can do is direct you to the support pages.
MapObjects 2.4 was last supported with ArcSDE 9.2. Oracle 11g support did not begin until ArcSDE 9.3.
What was supported with what is of limited use, because support for MapObjects 2.4 ended in July 2010
(MO 2.3 support ended in 2007), Oracle's support for 10gR2 ended in May 2010, and ArcSDE 9.2 support
ends with 10.1 release this summer, so you're still deep in Unsupportedland.
You can prototype the upgrade to see if it might work (some 9.2 ArcSDE clients [post SP4] were supported
to connect to 9.3/9.3.1 ArcSDE servers, so there's some hope), but it's probably not wise to pursue a full
upgrade if your app doesn't work perfectly under rigorous testing on a modern host running 9.3.1SP2 on
Oracle 11.1.0.2.
I should also point out that ArcSDE 9.3 won't function without a license key, so you'll need to engage
your local Esri office to get the evaluation license to test this configuration.
- V