A maioria dos exemplos de soquete de rede que encontrei para o Android eram apenas um direcionais. Eu precisava de uma solução para um fluxo de dados bidirecional. Acabei aprendendo sobre o AsyncTask. Este exemplo mostra como obter dados de um soquete e enviar dados de volta para ele. Devido à natureza de bloqueio de um soquete que está recebendo dados, esse bloqueio precisa ser executado em um thread diferente do thread da interface do usuário.

Por uma questão de exemplo, esse código se conecta a um servidor da web. Pressionar o botão "Iniciar AsyncTask" abrirá o soquete. Uma vez aberto o soquete, o servidor da web aguarda uma solicitação. Pressionar o botão "Enviar mensagem" enviará uma solicitação ao servidor. Qualquer resposta do servidor será exibida no TextView. No caso do http, um servidor da web será desconectado do cliente assim que todos os dados forem enviados. Para outros fluxos de dados TCP, a conexão permanecerá ativa até que um lado seja desconectado.

Captura de tela:

AndroidManifest.xml:

<?xml version="1.0" encoding="utf-8"?>
<manifest xmlns:android="http://schemas.android.com/apk/res/android"
      package="com.exampleasynctask"
      android:versionCode="1"
      android:versionName="1.0">
    <uses-sdk android:minSdkVersion="8" />
    <uses-permission android:name="android.permission.INTERNET" />
    <application android:icon="@drawable/icon" android:label="@string/app_name">
        <activity android:name=".MainActivity"
                  android:label="@string/app_name">
            <intent-filter>
                <action android:name="android.intent.action.MAIN" />
                <category android:name="android.intent.category.LAUNCHER" />
            </intent-filter>
        </activity>
    </application>
</manifest>

res \ layout \ main.xml:

<?xml version="1.0" encoding="utf-8"?>
<LinearLayout xmlns:android="http://schemas.android.com/apk/res/android"
    android:orientation="vertical"
    android:layout_width="fill_parent"
    android:layout_height="fill_parent"
    >
<Button android:id="@+id/btnStart" android:layout_width="wrap_content" android:layout_height="wrap_content" android:text="Start AsyncTask"></Button>
<Button android:id="@+id/btnSend" android:layout_width="wrap_content" android:layout_height="wrap_content" android:text="Send Message"></Button>
<TextView android:id="@+id/textStatus" android:textSize="24sp" android:layout_width="fill_parent" android:layout_height="wrap_content" android:text="Status Goes Here" />
</LinearLayout>

src \ com.exampleasynctask \ MainActivity.java:

package com.exampleasynctask;

import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.net.InetSocketAddress;
import java.net.Socket;
import java.net.SocketAddress;

import android.app.Activity;
import android.os.AsyncTask;
import android.os.Bundle;
import android.util.Log;
import android.view.View;
import android.view.View.OnClickListener;
import android.widget.Button;
import android.widget.TextView;

public class MainActivity extends Activity {
    Button btnStart, btnSend;
    TextView textStatus;
    NetworkTask networktask;

    @Override
    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.main);
        btnStart = (Button)findViewById(R.id.btnStart);
        btnSend = (Button)findViewById(R.id.btnSend);
        textStatus = (TextView)findViewById(R.id.textStatus);
        btnStart.setOnClickListener(btnStartListener);
        btnSend.setOnClickListener(btnSendListener);
        networktask = new NetworkTask(); //Create initial instance so SendDataToNetwork doesn't throw an error.
    }

    private OnClickListener btnStartListener = new OnClickListener() {
        public void onClick(View v){
            btnStart.setVisibility(View.INVISIBLE);
            networktask = new NetworkTask(); //New instance of NetworkTask
            networktask.execute();
        }
    };
    private OnClickListener btnSendListener = new OnClickListener() {
        public void onClick(View v){
            textStatus.setText("Sending Message to AsyncTask.");
            networktask.SendDataToNetwork("GET / HTTP/1.1\r\n\r\n");
        }
    };

    public class NetworkTask extends ,AsyncTask<Void, byte[], Boolean> {
        Socket nsocket; //Network Socket
        InputStream nis; //Network Input Stream
        OutputStream nos; //Network Output Stream

        @Override
        protected void onPreExecute() {
            Log.i("AsyncTask", "onPreExecute");
        }

        @Override
        protected Boolean doInBackground(Void... params) { //This runs on a different thread
            boolean result = false;
            try {
                Log.i("AsyncTask", "doInBackground: Creating socket");
                SocketAddress sockaddr = new InetSocketAddress("192.168.1.1", 80);
                nsocket = new Socket();
                nsocket.connect(sockaddr, 5000); //10 second connection timeout
                if (nsocket.isConnected()) { 
                    nis = nsocket.getInputStream();
                    nos = nsocket.getOutputStream();
                    Log.i("AsyncTask", "doInBackground: Socket created, streams assigned");
                    Log.i("AsyncTask", "doInBackground: Waiting for inital data...");
                    byte[] buffer = new byte[4096];
                    int read = nis.read(buffer, 0, 4096); //This is blocking
                    while(read != -1){
                        byte[] tempdata = new byte[read];
                        System.arraycopy(buffer, 0, tempdata, 0, read);
                        publishProgress(tempdata);
                        Log.i("AsyncTask", "doInBackground: Got some data");
                        read = nis.read(buffer, 0, 4096); //This is blocking
                    }
                }
            } catch (IOException e) {
                e.printStackTrace();
                Log.i("AsyncTask", "doInBackground: IOException");
                result = true;
            } catch (Exception e) {
                e.printStackTrace();
                Log.i("AsyncTask", "doInBackground: Exception");
                result = true;
            } finally {
                try {
                    nis.close();
                    nos.close();
                    nsocket.close();
                } catch (IOException e) {
                    e.printStackTrace();
                } catch (Exception e) {
                    e.printStackTrace();
                }
                Log.i("AsyncTask", "doInBackground: Finished");
            }
            return result;
        }

        public void SendDataToNetwork(String cmd) { //You run this from the main thread.
            try {
                if (nsocket.isConnected()) {
                    Log.i("AsyncTask", "SendDataToNetwork: Writing received message to socket");
                    nos.write(cmd.getBytes());
                } else {
                    Log.i("AsyncTask", "SendDataToNetwork: Cannot send message. Socket is closed");
                }
            } catch (Exception e) {
                Log.i("AsyncTask", "SendDataToNetwork: Message send failed. Caught an exception");
            }
        }

        @Override
        protected void onProgressUpdate(byte[]... values) {
            if (values.length > 0) {
                Log.i("AsyncTask", "onProgressUpdate: " + values[0].length + " bytes received.");
                textStatus.setText(new String(values[0]));
            }
        }
        @Override
        protected void onCancelled() {
            Log.i("AsyncTask", "Cancelled.");
            btnStart.setVisibility(View.VISIBLE);
        }
        @Override
        protected void onPostExecute(Boolean result) {
            if (result) {
                Log.i("AsyncTask", "onPostExecute: Completed with an Error.");
                textStatus.setText("There was a connection error.");
            } else {
                Log.i("AsyncTask", "onPostExecute: Completed.");
            }
            btnStart.setVisibility(View.VISIBLE);
        }
    }

    @Override
    protected void onDestroy() {
        super.onDestroy();
        networktask.cancel(true); //In case the task is currently running
    }
}