After digging around for about a day on this issue, I brazenly tried running ODI as the root user on the off chance that this was a permissions issue. I started ODI from the command line (using 'bash odi') for greater verbosity, and it loaded without the error mentioned above. Something gave me the impression that this wasn't a permissions issue, but one related to the user settings.
To rectify the issue, I removed my user's odi settings folder (renaming it, for safety):
mv ~/.odi ~/.backup_odi
Then I started ODI from the terminal under my own user (i.e. not root) - there were no errors! None of my connections were available in the new settings folder though. This I fixed by closing ODI and entering the following:
cp ~/.backup_odi/oracledi/snps_login_work.xml ~/.odi/oracledi/
If anybody else encounters this issue, I hope you find this post quicker than it took me to fix it!