I recently worked with a client who had an unusual dislike of conducting business on the phone, which became especially intense when talking with someone she didn't know.
In an interesting coincidence, I struggle with the same situation. Email? In person? I'm fine striking up a conversation with someone I don't know. A phone call coming in from a number I don't recognize? I don't want to answer it, and I often feel awkward with my wording as I'm speaking.
Recently I stumbled upon a way to make these calls much, much easier. I thought I'd share my discovery in case there are others out there who struggle as my client and I do.
First I let new calls from unknown sources go to voice mail. I then prepare myself and call the person back. Immediately after I dial, I stand up and pace slowly while talking.
Keep your arms uncrossed and hands out of your pockets ("open" body language). If you pace then be sure to keep it slow; when I've paced too quickly I became out-of-breath and struggled to talk evenly. Feel free to gesture with your hands as if the person were in the room with you.
I can't explain why this works, I have no brilliant theories. All I know is that I feel less "trapped" when I talk to strangers on the phone this way, and my ability to find words, answer questions, and be flexible and nimble with my ideas are much improved when I stand, walk, and gesture while talking.
If you find these kinds of phone calls challenging then give this technique a try.