I created a webservice on my local machine and connect to it with localhost. The webservice works great when I access it via IE and I am able to do all the functions created with no problem. When I create a script to access the webservice via powershell I get the following error. If I access an outside webservice like get teh weather powershell works just fine.
Your web server seems to be configured strangely. If you look at the URL of the "Object moved HERE" text, you see it is trying to redirect you to API/webservice.asmx?AspxAutoDetectCookieSupport=1. That seems strange, since a web service shouldn't need cookies, unless your service needs them. IE probably handles this because its a full-blown browser with cookie support. I would guess Invoke-WebRequest doesn't work that way.