If you have ssh set up the messages should not appear unless the terminal monitor command has been used. If you know the passwords for the ssh connections use those. Then input the no logging command.
www.cisco.com/en/US/docs/security/pix/pi...emint.html#wp1022084
Good luck.
Also try ctrl+z and ctrl+shift+6.
Honesty my firewall troubleshooting knowlgege is a bit less then many of the people here but I've been in that spot before so I'm giving you the advice that I would attempt.
edit: upon further review it appears you do not have nat/pat setup correctly and your getting that spam because hosts on your network error out when trying to get out of the network. When everyone goes home unplug the traffic generating units from the security device it should knock down the number of error messages to zero and you should be able to work with a prompt. If the network your working with is a highly important network with crucial uptime I suggest looking to a local firm to consult in. The disadvantage is the consultant is likely to be charging 1 arm and 1 leg the advantages are however you will likely make the difference up in the cost of the rest of the staff who are being paid to do nothing with the difference in downtime spent by you and the consultant and you will likely take less stress from your manager for something that has more or less been thrown into your lap. Additionally check around and see if there are any backup config files for the ASA. It's quite possible the ex-employee intentionally removed the nat configuration or changed it. If there is a backup laying around or on a tftp server somewhere use it. But only after copying the current startup and running configs to a tftpserver.
EDIT Summary: get someone from outside to do it you don't want to take shit for someone elses mess
Try to copy the current running and startup configs to a tftp server.
If possible try to work on it when nobody else is there (assuming you can't get a consultant) and remove sources of traffic.
Note: more then likely you won't have to disconnect any wires just shut off the device that connects the hosts to the ASA.
