Well I have good and bad news.
The good news is, there is something called the 'Unified API' NCH has developed to help developers have more control over many of NCH's applications. Axon is shown as one of the compatible applications for this, and the API web page goes all the way to give this example: "What if you want to setup an extension in Axon for a specific time? Simply using the Windows Scheduler and the Unified API to send a command to Axon informing it to setup the appropriate extension."
The other good news is the API kit has pre-written examples for all sorts of programming languages, including VB.
The bad news is, I cannot find a single reference to the API on the Axon page, nor can I find any documentation on what commands are available for controlling Axon. The Unified API page says that there should be documentation on how to use the API on the web page for that software, but Axon's page has no such link.