We have a cheap $5/mo server at Godaddy as the "middle man" for these kinds of operations.
It works great, although not necessary if you have access to Linux servers as you said.
We are calling the API for a dozen different functions, on a regular basis, using cron jobs in Linux and executing cURL through PHP and MySQL. You could accomplish this using any scripting language you like!
We also have a few different software products running on Microsoft servers in the office that communicate with Volusion as well.
You are able to create server-side ASP pages, but the functionality is limited.
Here is a basic example in PHP:
$url = 'http://www.yoursite.com/net/WebService.aspx?Login=USERNAME&EncryptedPassword=PASSWORD&Import=Update';
$xml = 'YOUR COMPLETE XML';
$ch = curl_init();
curl_setopt($ch, CURLOPT_URL, $url);
curl_setopt($ch, CURLOPT_HEADER, FALSE);
curl_setopt($ch, CURLOPT_RETURNTRANSFER, TRUE);
curl_setopt($ch, CURLOPT_POST, TRUE);
curl_setopt($ch, CURLOPT_POSTFIELDS, $xml);
curl_setopt($ch, CURLOPT_HTTPHEADER, array("Content-Type:application/x-www-form-urlencoded; charset=utf-8", "Content-Action:Volusion_API"));
$head = curl_exec($ch);
$httpCode = curl_getinfo($ch, CURLINFO_HTTP_CODE);
curl_close($ch);