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1.
noun: a threesome. Technically a threesome of any kind, but more recently it has been used in a sexual manner.
Bob: "You look tired, what were you up to last night?"
Bill: "Remember those two girls from the club? We had a troika last night."
Bob: "Niiice..."
by logophilito November 12, 2007
 
2.
A mounted turret in any FPS game, such as Gears of War, and Call of Duty.
"Hey guys, you see that? That's me on the troika"
"Wow, you mowed them down"
by OM-GUH Holy Diver February 26, 2009
 
3.
In the sovereign debt crisis, beginning approximately in 2009, in the European region which uses the Euro as currency, three institutions, the European Central Bank (ECB), the European Commission (EC), and the International Monetary Fund (IMF) have taken the responsibility of monitoring the crisis and making policy recommendations. Collectively, these three are, sometimes irreverently, called the Troika.
From the blog www.nakedcapitalism.com, March 4, 2013:

"Even though we were keen about how voter repudiation of austerity in the Italian elections last week was throwing a wrench in the Troika’s austerity plans, we also warned, based on the example of Greece, that they’d try to neutralize the results."
by metrodorus March 05, 2013