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India, May 14 -- Dhoni was right in one way. Players have to make their own choices about their bodies, but it's not always that easy - not if you're not Mahendra Singh Dhoni or Sachin Tendulkar or Rahul Dravid.
My problem with the IPL Nites parties was not that I was forced to attend by any contractual obligation. There was no such thing for me, or, to my knowledge, for any of my fellow India players.
Each party was invariably the same routine. You would have a set-up with a ramp show that lasted 30 to 45 minutes, then the models would come off and mix with the rest and the party would take off.
There were cheerleaders and girls who we called 'escort service'. Beautiful women to add glamour to the mix, get the party moving. They were not allowed to talk to any player for more than five minutes. If they did, a manager would walk up and slickly move her away.

Please explain to me the emboldened parts.

Though I guess here "come off" means simply come i.e. "The models would come".

Source : http://in.news.yahoo.com/32/20100514/1073/tsp-ipl-parties-the-inside-story_1.html
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Actually "if something comes off, it succeeds as planned". But in your context it would be more of just "to occur".

http://dictionary.reference.com/browse/come

Meaning 58.
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I understand "come off" to mean get down from the ramp (catwalk).