Using org.json library:

try {
     JSONObject jsonObject = new JSONObject("{\"phonetype\":\"N95\",\"cat\":\"WP\"}");
}catch (JSONException err){
     Log.d("Error", err.toString());
}

There is a built-in method to convert a JSONObject to a String. Why don't you use that:

JSONObject json = new JSONObject();

json.toString();

See my comment. You need to include the full org.json library when running as android.jar only contains stubs to compile against.

In addition, you must remove the two instances of extra } in your JSON data following longitude.

   private final static String JSON_DATA =
     "{" 
   + "  \"geodata\": [" 
   + "    {" 
   + "      \"id\": \"1\"," 
   + "      \"name\": \"Julie Sherman\","                  
   + "      \"gender\" : \"female\"," 
   + "      \"latitude\" : \"37.33774833333334\"," 
   + "      \"longitude\" : \"-121.88670166666667\""
   + "    }," 
   + "    {" 
   + "      \"id\": \"2\"," 
   + "      \"name\": \"Johnny Depp\","          
   + "      \"gender\" : \"male\"," 
   + "      \"latitude\" : \"37.336453\"," 
   + "      \"longitude\" : \"-121.884985\""
   + "    }" 
   + "  ]" 
   + "}"; 

Apart from that, geodata is in fact not a JSONObject but a JSONArray.

Here is the fully working and tested corrected code:

import org.json.JSONArray;
import org.json.JSONException;
import org.json.JSONObject;

public class ShowActivity {


  private final static String JSON_DATA =
     "{" 
   + "  \"geodata\": [" 
   + "    {" 
   + "      \"id\": \"1\"," 
   + "      \"name\": \"Julie Sherman\","                  
   + "      \"gender\" : \"female\"," 
   + "      \"latitude\" : \"37.33774833333334\"," 
   + "      \"longitude\" : \"-121.88670166666667\""
   + "    }," 
   + "    {" 
   + "      \"id\": \"2\"," 
   + "      \"name\": \"Johnny Depp\","          
   + "      \"gender\" : \"male\"," 
   + "      \"latitude\" : \"37.336453\"," 
   + "      \"longitude\" : \"-121.884985\""
   + "    }" 
   + "  ]" 
   + "}"; 

  public static void main(final String[] argv) throws JSONException {
    final JSONObject obj = new JSONObject(JSON_DATA);
    final JSONArray geodata = obj.getJSONArray("geodata");
    final int n = geodata.length();
    for (int i = 0; i < n; ++i) {
      final JSONObject person = geodata.getJSONObject(i);
      System.out.println(person.getInt("id"));
      System.out.println(person.getString("name"));
      System.out.println(person.getString("gender"));
      System.out.println(person.getDouble("latitude"));
      System.out.println(person.getDouble("longitude"));
    }
  }
}

Here's the output:

C:\dev\scrap>java -cp json.jar;. ShowActivity
1
Julie Sherman
female
37.33774833333334
-121.88670166666667
2
Johnny Depp
male
37.336453
-121.884985