here is what i have... finally. just want to share and... correct me if i am wrong.

case 1.
- backup control file, backup dbf files, archives and the latest online redo log
- recover database using backup controlfile until cancel
- recover up to point of failure
- need to apply the online redo log manually
- incomplete recovery and need to open resetlogs

case 2
- backup control file, backup dbf files, archives and lost latest online redo log
- recover database using backup controlfile until cancel
- recover up to latest archive log
- incomplete recovery and need to open resetlogs

case 3
- latest control file, backup dbf files, archives and lost latest online redo log
- recover database until cancel
- recover up to latest archive log
- incomplete recovery and need to open resetlogs

case 4
- latest control file, backup dbf files, archives and the latest online redo log
- recover database until cancel
- recover up to point of failure
- complete recovery and online redo logs will be applied automatically