Hi,
Sorry for the issues. I am not sure I can help out here.
Transients can be setup by any plugin, theme, or custom coding to store information.
I have not seen an issue with our plugins causing this issue, but I can try to help on this, but I am limited.
Can you use a plugin like Transients Manager
Transients Manager
That will show you all the Transients and you can delete them.
Another option is Delete Expired Transients
Delete Expired Transients
That might help clear a lot of those out.
Another option might to use some sql to delete all the transients:
http://stackoverflow.com/a/11995022
It sounds like that should work, but I do not know the exact repercussions.
It would be a good idea to backup before altering the database in anyway.
Thanks