JBoss does not have a SOAP extension of its own. Most (if not all) SOAP implementations are tied to the delivery mechanism (HTTP), so they are usually coupled with the servlet container in the Java world. JBoss is only providing a wrapper service for starting the web service infrastructure (Axis) and deploying web services to it. You could choose to implement vanilla SOAP within Tomcat or Jetty embedded in JBoss as you would with stand-alone servlet containers. However, Axis is tagged as SOAP 3 and has a richer API set for working with data and services.
If you are wanting to provide web services to things other than Java clients or don't have Java data-type mapping, the you can use the Axis document or message service-type, rather than the RPC service-type. The choice will depend on your client and the most natural (and simplest) way for it to serialize parameters and deserialize results (returned data).
Refer to the Axis documentation and sample code for more information (especially the sample code as the docs are very sparse).
Can we use Axis with JBoss/Jetty or JBoss/Tomcat by just dropping the Axis directory structure into a deployment directory?
I assume I'd use the catalina/webapps directory for this? Or would I use server/default?
You can drop Axis in the deployment directory. However, JBoss.NET provides you with automated deployment of services so you may find that easier in at least the development stage of things. JBoss.NET is a service wrapper for Axis. If you are running the default instance of JBoss, just copy the jboss-net.sar directory and its contents from the server/all/deploy directory into server/default/deploy.
This tutorial on web service packaging the JBoss.NET way should help.