iRule append URi based on URL

This is quite simple - it will append the host header to the original URL. You can split up the host header with getfield eg set append [getfield [HTTP::host] "." 1]

when HTTP_REQUEST {
    set original_uri [HTTP::uri]
    set append [HTTP::host]
    set HTTP::uri "$original_uri/$append"
}

when HTTP_REQUEST {
    set original_uri [HTTP::uri]
    set append [getfield [HTTP::host] "." 1]
    set HTTP::uri "$original_uri/$append"
}

You seem to have used switch with else here, and two "when HTTP_REQUEST"s. Might be best to write this in pseudocode first and build the syntax from there. Does this match what you want?

when HTTP_REQUEST {
    if HTTP::host == owamail.test.com.au                
        then set HTTP::uri to /owa[HTTP::uri]
    elseif  HTTP::host == mobile.test.com.au                
        then set HTTP::uri to /Microsoft-Server-ActiveSync[HTTP::uri]
    endif
}

OK, so this is the iRule that implements that pseudocode:

when HTTP_REQUEST {
    if { [HTTP::host] equals "owamail.test.com.au"} {               
        set HTTP::uri /owa[HTTP::uri]
    } elseif  { [HTTP::host] equals "mobile.test.com.au"} {                
        set HTTP::uri /Microsoft-Server-ActiveSync[HTTP::uri]
    } 
}