How can I call a script query from external aplication

You say you want to update the spreadsheet from say a chrome extension. You can expose your update function using ContentService from within your script and then call that URL from your extension. Here's an example that sets data in a spreadsheet cell and returns a message:

function doGet(request) {

//get the data from the request's "somedata" querystring parameter ..../exec?somedata=mydata
var data = request.parameters.somedata;

//update the bound spreadsheet (workaround https://code.google.com/p/google-apps-script-issues/issues/detail?id=5734)
SpreadsheetApp.openById('1cm6tK0Io4lnbRZ0OhlvZijhrQoqCt01adyYlUbZgUZY')
.getSheetByName('Sheet1')
.getRange('B1')
.setValue(data);

//send some data back as a response
var result = {
data: 'Thanks, I received: ' + data,
error: null
};
return ContentService.createTextOutput(JSON.stringify(result))
.setMimeType(ContentService.MimeType.JSON);
}
To test:

In the code editor, Publish > Deploy as Web App
Choose Execute the app as me, Allow access: anyone, even anonymous
Click Deploy, then Authorise and Allow.
Copy and note the URL that is given. I got https: //script.google.com/macros/s/AKfycbyTi0NOZdTm5J_tZnUXw9skWfYlLADvkDDdCd593XC-H6LN4A/exec
Add ?somedata=ABC123 to the URL and hit the full URL from an incognito browser window. https://script.google.com/macros/s/AKfycbyTi0NOZdTm5J_tZnUXw9skWfYlLADvkDDdCd593XC-H6LN4A/exec?somedata=ABC123
This results in "ABC123" being set in cell B1 and the browser message: {"data":"Thanks, I received: ABC123","error":null}

Here's a link to the source spreadsheet from which you can File > Make a copy.

It will very much depend on the external application you are using. As you mentioned you can use PS to query the Orion API. This could be done on-demand, or via a scheduled task etc.  What methods for data import are available on your external App? Does it have an API? Can it import structured data through the UI?

the idea is to access from the external app to the API. https://solarwinds.main.server:17778/SolarWinds/InformationService/v3/Json/  

consulting the information, i was doing querys directly like this: 

https://solarwinds.apiserver:17778/SolarWinds/InformationService/v3/Json/Query?query=SELECT Caption, IPAddress FROM Orion.Nodes WHERE Vendor = 'Cisco'

but i need to authenticate the connection, and cant put the credentials on the link. that's is the reason I'm trying to use PS. 

thanks for trying to help me.