Toastmasters helped me with conversation a lot. Especially the "table topics" part of the meeting. Highly recommended.

Seconding Toastmasters, great excuse to meet people at work outside of your department.

I like this answer because it starts with finding a setting that the other strangers chose likely to meet some strangers, instead of finding ways to lock some random person in a conversation. It's the first sign of basic respect that can, in my eye, excuse _a lot_ of awkwardness.