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.