Ι've tried all the solution that I could find, but nothing seems to work:

teext = str(self.tableWidget.item(row, col).text())

I'm writing in greek by the way...

Clearly, self.tableWidget.item().text() returns Unicode, and you need to use the decode method instead:

self.tableWidget.item(row, col).text().encode('utf8')

You really want to review the Python Unicode HOWTO to fully appreciate the difference between a unicode object and it's byte encoding.

Another excellent article is The Absolute Minimum Every Software Developer Absolutely, Positively Must Know About Unicode and Character Sets (No Excuses!), by Joel Spolsky (one of the people behind Stack Overflow).