Didn't try but in VS add this Oracle.ManagedDataAccess.dll reference by browse. Set Copy to output directory.
Verify if it runs ok.
It looks to me that is t should work, like with log4net.dll 🙂
Don't deploy your AddIn by AddInManager but, by hand, by copying it in well known locations like C:\Program Files\ArcGIS\Desktop10.0\Bin\Addins\ with Oracle.ManagedDataAccess.dll
Please try and let us know does it hold water.
Regards Dubravko