I want to know if there is any way I can make or catch calls while sitting on a Windows Client machine. Actually what I want is may be some SDK which can be used to intercep calls or make calls using that API on a network with trixbox/PBXtra installation.
FreePBX has nothing to do with PBXtra, no relation at all. So your request is a bit confusing. (It’s even confusing what you want to do even if you replaced PBXtra with FreePBX in your question).
What are you trying to accomplish?
Perhaps a softphone like x-lite would do what you want?