It sounds as though you want to do a normal HTTP POST to your server. It's the same thing that would happen when you fill out a form on a web-page and submit the data to a server. If it's a normal kind of webserver it should have full support for receiving a POST and returning a response as well. Are you writing the .NET web service as well?
As for client side technology to use: OkHTTP is a greaty drop-in class for making HTTP requests to a server, but if you plan to do many of them you should also look into wrapping the actual HTTP client into an API that takes care of asynchronous callbacks and things like that. You don't want to be doing HTTP requests on the UI thread and it's boring and error prone to wrap all such calls in AsyncTasks or similar. Take a look at AndroidAsyncHttpClient:
"An asynchronous callback-based Http client for Android built on top of Apache’s HttpClient libraries. All requests are made outside of your app’s main UI thread, but any callback logic will be executed on the same thread as the callback was created using Android’s Handler message passing."
(As a sidenote AndroidAsyncHttpClient might get support for using OkHTTP instead of the default Apache HttpClient)
POSTing to a server is as simple as this:
RequestParams params = new RequestParams();
params.put("A_KEY_TO_IDENTIFY_YOUR_STRING", "THE_STRING_YOU_WANT_TO_SEND");
AsyncHttpClient client = new AsyncHttpClient();
client.post("http://www.yourserver.com", params, new AsyncHttpResponseHandler() {
@Override
public void onSuccess(String response) {
// handle your response from the server here
System.out.println(response);
}
});