If the question was "Is it possible to do the task using any of these methods?" then the simple answer is yes.
VoiceXML lets you define an application executed on a VoicePlatform like Cisco CVP, Avaya AVP, Genesys GVP, ... The only "issue" which you will have is that you need one of those for it (and they tend to be relatively expensive).
If you had a speech recognizer and a speech synthesis engine then you may be able to have calls coming into an Astrisk platform and sending these via SIP into a SIP-capable server which builds the dialog in any programming language you like (e.g. Java). Here you'll need a speech recognizer and a speech synthesis engine to do the "conversions".
Even though my answer implies it is simple, there are many issues to overcome on the way, like: speech quality, recognition accuracy, error handling, etc.