In order to use ExQuilla, you must have access to an Exchange server that has Exchange Web Services (EWS) enabled. In most cases, this will be located using ExQuilla's autodiscover functionality. If autodiscover fails, then the most likely scenario is that your server does not support Exchange Web Services, and you cannot use ExQuilla. Sorry about that.
But if you believe that you have a valid EWS url, you can enter it manually. You can also test your manual URL to make sure that it is valid. To see if, for example, the EWS URL https://webmail04.domainlocalhost.com/EWS/Exchange.asmx is valid, enter that into a web browser. You should get a screen asking for a name and password. If you successfully enter a name and password, then the browser should display some XML that has as its first line:
If you cannot get this to work, then your manual EWS URL is invalid, and will not work with ExQuilla.
You can see the EWS URL that ExQuilla is using from the screen Tools/Account Settings/(Your Exchange Account)/Microsoft Exchange Server/"Microsoft Exchange EWS URL".
You may also use Microsoft's connectivity analyzer at https://testconnectivity.microsoft.com/ To use this, choose "Synchronization, Notification, Availability, and Automatic Replies" on the "Exchange Server" tab. In most cases, if you can get this to demonstrate EWS connectivity, then ExQuilla should work. On the results page for that, there is a small icon with the tooltip "Save as HTML" which can save the results of this. If you want ExQuilla to comment on your results, it would be good to save that to HTML and then attach the results to a support request.