Recovery from datafiles
Right,

For anyone else who might come across this post - I am just adding this information for the sake of completeness. 

It took me a long time to get this sorted. I booted off of a SystemRescueCD and ran testdisk. It managed to recover my LVM partitions, which I couldn't mount due to damage to the disks. I tried numerous file recovery tools. R-Studio was probably the most helpful, it managed to recover file fragments. 
I also ran Scalpel version 2.0. This version allows for specification of minimum file size, which was important in my case since I knew how big the files were. Scalpel took roughly 3 days, but we managed to recover our 5 data files. However without any of the other files (controlfiles, archived redo logs etc) recovery was still a challenge. I managed to create new controlfiles and rebuild the spfile from a previous copy of the pfile. I ended up starting the database with resetlogs. So no far we haven't had any reports of missing data. 

We were incredibly lucky. While I would say that even in the worst imaginable scenario there might be hope for recovery, it is in no way an excuse to eschew prescribed backup methods. I cannot overstate how lucky we were that we managed to salvage our data, after having to deal with a malfunctioning RAID controller, corrupt partitions and missing files. My employers have now taken a more serious and pragmatic view towards offsite backups. but I wouldn't want to see anyone in this position. Like they say - prevention is better than cure.

For reference :
Oracle Data File Headers in Hex : 00 A2 00 00 FF C0 ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? ?? 7A 7B 7C 7D
Oracle Data File Footer : 00 00 00 01
The question marks represent characters which will be different for every data file. Scalpel allows you to specify wildcards. 
R-Studio also allows defining a specific file type and searching for that file type, but I didn't try it.

Thanks to everyone who took time to share their advice. I am grateful to you all.

Regards

Alex