If you have setup a Web API service using the basic, default configurations that the MS walkthroughs suggest, then the response formatter is already configured and will use json by default, or xml if so prompted.
So the prompt for an xml response usually comes from the client request. At its basic form, the request will contain a Accept: application/atom+xml,application/xml
header. If it does not, I believe the Web API response will default to json.
For your particular question, there is an alternative for LinqPad. When you setup your OData connection, the dialog has a Formatter
option of Xml or Json, which tells Linqpad to issue the corresponding Accept header in its request.
Using Fiddler to monitor the traffic, if you set the LinqPad OData connection to use the xml formatter, the request contains the headers:
MaxDataServiceVersion: 3.0;NetFx
Accept: application/atom+xml,application/xml
and the response comes back as an atom/xml feed.
If you set the option to use the json formatter, the request contains the headers:
MaxDataServiceVersion: 3.0;NetFx
Accept: application/json;odata=minimalmetadata
and the response comes back as json.
For oData v3, LinqPad handles both just fine.
Edit
This now sounds vaguely familiar with some test I ran a short time ago...I'm not sure if LinqPad supports the v4 protocol yet. It uses WCF Data Services client under the covers, and those libraries stopped at OData v3. And, in fact, as you see from the headers above, the request will only talk to a v3 service.
So your issue is not that the Web Api is not supporting both xml and json. The issue is that LinqPad does not yet connect to a v4 oData service. Using Fiddler or other similar tool, you should be able to request both json and/or xml from the service.