All are okay, but not necessarily interchangeable. I’d use different ones for different situations.
Sounds like he’s busy doing something else, and just isn’t answering anybody’s calls. (I wouldn’t use this for mobile phones, no)
Sounds like your calls are being purposely screened by his secretary.
Sounds like he’s looking at the caller ID and not answering your call (but is answering calls from other people.)
Similar to # 2. A third person is informing him that you’re calling, and he’s told that person he doesn’t want to talk to you.
Another alternative along these lines is simply “He’s not answering.” This just means you’re calling, and he’s not answering. Nothing is implied as to why he’s not answering.