I want to use KMyMoney both at home and work. How can I synchronize its work in several geographically-spread places? Is there some internal instruments?

The best way for me would be something like mail in IMAP and address book in Kolab/imap.

There is no such mechanism. It should be easily syncable because it's just a XML file, but I would send it compressed and encrypted over email.

A pen drive is out of the question, right?

In case you have online access to the file at home: you could use any KIO mechanism (sftp://, fish://, ...) to open a file from a network location. Just make sure one instance has the file open at a time.