This is very strange, your database must have got corrupted somehow. You will probably need to uninstall JoomSEF and install it again. If you don't want to lose your URLs, export them first using the Manage SEF URLs page, and import them again after the new installation.
Or we can try to fix the database first if you want - in that case, use some MySQL manager (phpMyAdmin for example), find the jos_sefurls table in your database and post its structure (field names and types).
Best regards,
ARTIO Support Team