Apache httpd Redirecting URL based upon Server Name

We have a Jira and a Confluence system at my work. Both are running on the same servers. The actual URL to access Jira and Confluence are:

http://foauslxapp05:8080/jira
http;//foauslxapp05:8090/confluence

or with the fully qualified host name:

http://foauslxapp05.foservices.corp:8080/jira
http://foauslxapp05.foservices.corp:8090/confluence

To simplify everything, I've setup a proxy rule to allow users to do this:

http://foauslxapp05/jira  <-- Accessing Jira
http://foauslxapp06/wiki  <-- Accessing Confluence

Our techs have created pair of server aliases for foauslxapp05, so that:

http://jira/jira     <-- Accessing Jira
http://jira.foservices.corp/jira  <-- Accessing Jira
http://wiki/wiki     <-- Accessing Confluence
http://wiki.foservices.corp/wiki  <-- Accessing Confluence

What I'd really like to do is take this to the next step:

http://jira    <-- Accessing Jira
http://jira.foservices.corp  <-- Accessing Jira
http://wiki    <-- Accessing Confluence
http://wiki.foservices.copr  <-- Accessing Confluence

The problem, of course, is that the DNS names jira and wiki are merely DNS aliases for foauslxapp05. I need to detect the URL that the user entered (i.e. what host the user requested), then based upon that URL, I need to redirect the user to the correct application.

I'm not even too sure what I should be looking at: Is this VirtualHost? mod_rewrite? mod_proxy? Or, is this something else entirely. I can't imagine something like this being too difficult to do. Unfortunately, I'm just not too familiar with Apache httpd.