Hi,
you should check what statements are eating your CPU.
But, as you are talking about having compressed some tables, execute the script Segments_Tables_CriticalCompressedTables_11g+ from note 1438410 and, if there is ANY table reported, then you should "uncompress it"
in addition, do you have at least, the SBP from February this Year?
If not, it is indicated on the HOTNEWS note 1847870 a long list of critical issues with table compression