Ok, it wasn't very clear in your post, but are you using some kind of FXO device?
Vonage has decided to lock all their devices so they can't be used with other services or software like Axon. This means, you are left with only 2 options:
1) Purchase Vonage's Softphone plan (this opens up your Vonage account so Axon can connect directly to it easily without any additional hardware) PRO: Easy CON: Costs involved, order in addition to normal Vonage plan)
OR
2) Using an FXO adaptor such as the SPA3000 OR SPA3102 PRO: No extra ongoing costs CON: Purchase cost, more difficult to set-up
(this means your Vonage VoIP line will be converted to a PSTN analogue line from the adaptor they gave you, and then sent to the FXO device which will then convert the analogue line back to a digital VoIP line and send it to Axon. Then you may have analogue phones you wish to connect to Axon with ATA adaptors which convert digital VoIP lines to analogue phone lines. A lot of unnecessary conversions, just because Vonage doesn't want you using other non-vonage hardware/software).