Dear Bob:
I did heavy duty Oracle administration. From the posts so far it appears that both your log files and the global area is not large enough for your database (just think that deleting 300K lines by 40 bytes adds 12MB to your journal each time where each transaction has to fit into the redo area (1MB)). Typical rule of thumb has always been that for a 40GB data set you need about 4GB of memory (10%) of which 40MB in the redo area, 1GB in the variable area and 1GB of database buffers. These type of errors can also occur if the data base is full. Another criteria is to keep the database area to be twice the size of the stored data (tables and indicies).
So the first thing is to backup the files. The fastest way to backup the files is to shutdown the system, mount a hard drive with enough space to hold all the files, boot the system and copy data from the current files to the new hard drive. Alternatively if you are using some logical volume management system is to extend the DB filesystem by adding additional physical areas to the logical group and proceed as above. This should copy at over 20-30MB/s using either method so should take no more than 30 minutes.
By the way, by using hot swap type IDE or SCSI trays (HD in a hot pluggable tray), this can be used as a method of taking fast snapshots of the database and then can be swapped with another drive tray and moved to a box that simply has a small HD, the hot swap tray and a tape/DVD-R backup unit to back up the data. Another more elaborate setup is to 3 way mirror (RAID 1) the database, then detach the 3rd way to backup from and then reattach to resync the 3rd mirror. This can be done without stopping the database at any time.
The next thing is to increase the size of your global area. The third is to add additional log files and/or make each bigger. You then should be able to mount/restore the database.
Pete