EOFException in your code

The problem seems to be your while (to.value != 1). The server receives the first object, with value 1. It does not execute that while loop at all, but instead closes the socket immediately. So when the client tries to create an ObjectInputStream from the input stream of that socket, it encounters a closed connection where it would expect an object stream header. Thus the EOFException.

Implementing a conversation

The easiest way to implement a conversation is avoiding the loops altogether. After all, you do the loop but then do a case distinction within the loop to execute special code in each pass. You might as well write a linear program, and factor common code into method calls if needed, although your example has little common code.

class SimpleClient {
    public static void main(String args[]) throws Exception {

        // Connection setup
        Socket s = new Socket("localhost",2002);
        OutputStream os = s.getOutputStream();
        ObjectOutputStream oos = new ObjectOutputStream(os);
        InputStream is = s.getInputStream();
        ObjectInputStream ois = new ObjectInputStream(is);
        testobject to;

        // Conversation

        System.out.println("sending object 1");
        to = new testobject(1,"object 1","field1","field2","field3","field4");
        oos.writeObject(to);

        System.out.println("receiving object 2");
        to = (testobject)ois.readObject();
        System.out.println(to.id);

        System.out.println("sending object 3");
        to = new testobject(2,"object 3","field1","field2","field3","field4");
        oos.writeObject(to);

        System.out.println("receiving object 4");
        to = (testobject)ois.readObject();
        System.out.println(to.id);

        // Connection shutdown
        ois.close();
        oos.close();
        s.close();
    }
}

class SimpleServer {
    public static void main(String args[]) throws Exception {

        // Connection setup
        ServerSocket ss = new ServerSocket(2002);
        Socket s = ss.accept(); // only handle a single connection
        ss.close(); // so we can immediately stop listening for more
        OutputStream os = s.getOutputStream();
        ObjectOutputStream oos = new ObjectOutputStream(os);
        InputStream is = s.getInputStream();
        ObjectInputStream ois = new ObjectInputStream(is);
        testobject to;

        // Conversation

        System.out.println("receiving object 1");
        to = (testobject)ois.readObject();
        System.out.println(to.id);

        System.out.println("sending object 2");
        to = new testobject(2,"object 2","field1","field2","field3","field4");
        oos.writeObject(to);

        System.out.println("receiving object 3");
        to = (testobject)ois.readObject();
        System.out.println(to.id);

        System.out.println("sending object 4");
        to = new testobject(4,"object 4","field1","field2","field3","field4");
        oos.writeObject(to);

        // Connection shutdown
        ois.close();
        oos.close();
        s.close();
    }
}

Send and receive queues

If you really want to send stuff from a queue, you can simply iterate over it.

import java.net.*;
import java.io.*;
import java.util.*;

class SimpleClient {
    public static void main(String args[]) throws Exception {

        // Preparing the queues
        List<testobject> sendQueue = Arrays.asList(
            new testobject(1,"object 1","field1","field2","field3","field4"),
            new testobject(2,"object 3","field1","field2","field3","field4"));
        List<testobject> receiveQueue = new ArrayList<testobject>();

        // Connection setup
        Socket s = new Socket("localhost",2002);
        OutputStream os = s.getOutputStream();
        ObjectOutputStream oos = new ObjectOutputStream(os);
        InputStream is = s.getInputStream();
        ObjectInputStream ois = new ObjectInputStream(is);
        testobject to;

        // Conversation, we start by sending
        for (testobject toSend: sendQueue) {
            System.out.println("Sending " + toSend.id);
            oos.writeObject(toSend);
            testobject received = (testobject)ois.readObject();
            System.out.println("Received " + received.id);
            receiveQueue.add(received);
        }

        // Connection shutdown
        ois.close();
        oos.close();
        s.close();
    }
}

class SimpleServer {
    public static void main(String args[]) throws Exception {

        // Preparing the queues
        List<testobject> sendQueue = Arrays.asList(
            new testobject(2,"object 2","field1","field2","field3","field4"),
            new testobject(4,"object 4","field1","field2","field3","field4"));
        List<testobject> receiveQueue = new ArrayList<testobject>();

        // Connection setup
        ServerSocket ss = new ServerSocket(2002);
        Socket s = ss.accept(); // only handle a single connection
        ss.close(); // so we can immediately stop listening for more
        OutputStream os = s.getOutputStream();
        ObjectOutputStream oos = new ObjectOutputStream(os);
        InputStream is = s.getInputStream();
        ObjectInputStream ois = new ObjectInputStream(is);
        testobject to;

        // Conversation, we start by receiving
        for (testobject toSend: sendQueue) {
            testobject received = (testobject)ois.readObject();
            System.out.println("Received " + received.id);
            receiveQueue.add(received);
            System.out.println("Sending " + toSend.id);
            oos.writeObject(toSend);
        }

        // Connection shutdown
        ois.close();
        oos.close();
        s.close();
    }
}

But since in this case, all the data is known up front, you might save some network round trips by not interleaving things, but instead sending all data at both ends immediately, using a separate thread to receive things. However, that would be even further away from your example, so I'll not include code for this.