If your database was running in archivelog mode and you have all of the archived log files you should be able to get the database back. You need to recreate the control file(s). You're going to do something like:
startup nomount
create controlfile set database "yourdb" archivelog
...
your datafiles and other settings
...
If you were backing up your control file to trace ('backup control file to trace') you will have a script (usually in your udump directory) you can start with, but it will need some minor tweaking.
Then you will roll forward through your log files. Even if you don't have everyone of them you may be able to get all the file headers synced in order to open Oracle.
recover database until cancel using backup controlfile
And finally open your database with
alter database open resetlogs
That's the basic idea anyway.
Good luck.
