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.