I have a PHP Toolkit script that updates fields on invoices and sales orders. How can I prevent other scripts from being triggered when my PHP Toolkit script makes these updates?

You can either exclude the SOAP Web Services context from each script which runs on the record you're updating, or you can turn off server scripts and workflows for individual SOAP requests. I'm not super familiar with the PHPToolkit, but it should look something like this:

$service = new NetSuiteService();
$preferences = new Preferences();

$preferences->runServerSuiteScriptAndTriggerWorkflows = false;

$server->setPreferences($preferences);