it's been awhile since we did this and my Oracle administrator probably remembers better, but I think we took a backup of the database on the old server and restored it on the new server, then did the Oracle upgrade, followed by the Geodatabase upgrade (do not forget to put the correct version of the shape library if using ESRI ST geometry on the new server). Also our Oracle administrator handled the TNS file update so our existin .sde connection files, layers, and MXDs were stable. Sorry, that isn't much detail.
I am primarily the SDE or geodatabase administrator and before we started made sure to compress the geodatabase versions down as much as possible by synchronizing all replicas and getting old versions removed or reconciled & posted to minimize size of delta tables
