Why are conversations with people you don't know weird?
What is it that makes you uncomfortable when you don't know someone? its like being unsure about anything always causes anxiety/stress. People avoid the stress (uncomfortableness?) at any cost. people wont do anything unless they are pretty close to sure they know how it will turn out. And the way they feel like its going to turn out has to suit their interests.
How can you get people to become more comfortable in conversations? Prolly become more comfortable yourself. Get enough experience in conversations that you are confident that what ever happens you will be able to deal with it, you wont have awkward pauses and that any conversation you get into is going to be fun and fulfilling. After you get that believe I'm sure you will transfer that state to the other person and help them get there as well.
People fear the unknown. In conversations the unknown is the next topic of discussion, how the person will interpret what your saying and how the person will respond. The fear comes from not knowing how your response will be judged. So as you build trust you can build a closer level on conversation.