eksi is an abbreviation for "
Enna koduma
sir idhu".
The orginal dialogue was
first used in the rajinikant starrer Chandramukhi and has been parodied ever since, most notably by premji in the tamil movie chennai-28.
Since then the phrase has become a frequenter in many tamil conversations and was subsequently abbreviated and moved in to the
sms lingo. It is usually used to express displeasure/unhappiness about something, showing some signs of grief and sometimes surprise.