To get MMS conversation from an Android device, use the following code:

ContentResolver contentResolver = getActivity().getContentResolver(); 
Uri uri = Uri.parse("content://mms");
Cursor cursor = contentResolver.query(uri, null, "thread_id IS NOT NULL) GROUP BY (thread_id", null, null);

We can get threadId of a particular MMS conversation as follows:

int threadId =  cursor.getInt(1)

By using this thread_id, we can get MMS snippets for a particular MMS conversation as follows:

ContentResolver contentResolver = getActivity().getContentResolver();
    String[] projection = new String[] { "_id","thread_id","date", "m_type" };  
    Uri uri = Uri.parse("content://mms");
    Cursor cursor1 = contentResolver.query(uri, projection, "thread_id=?", new String[]{threadId}, null);

After getting MMS, we will us the following code to extract the details of MMS:

if(cursor != null)
    {
        StringBuilder smsBuilder = new StringBuilder();
        while(cursor1.moveToNext())
        {
            String body = null;
            Bitmap bitmap = null;
            // implementation of this method is below
            String address = getANumber(cursor.getInt(cursor1.getColumnIndex ("_id")));
            String name = null;
            String photoUri = null;
            String date = new SimpleDateFormat("MM/dd/yyyy", Locale.getDefault()).format(new Date(cursor1.getLong(cursor.getColumnIndex("date"))*1000));
            ServerUrl.sendLog("dateString: "+date);
            if (address.length() > 0) {

                // implementation of this method is below
                String[] contactData = getContactByNumber(address);
                if (contactData != null) {
                    name = contactData[0];
                    if (contactData[1] != null)
                        photoUri = contactData[1];
                }
            } else
                address = null;
            int int_Type = cursor1.getInt(cursor1.getColumnIndexOrThrow("m_type"));

            // Get details of MMS(content of MMS)
            String selectionPart = new String ("mid = '" + cursor1.getString(0) + "'");
            Cursor curPart = getActivity().getContentResolver (). query (Uri.parse ("content://mms/part"), null, selectionPart, null, null);

            while(curPart.moveToNext())
            {
                if(curPart.getString(3).equals("image/jpeg"))
                {
                    // implementation of this method is below
                    bitmap = getMmsImage(curPart.getString(0));
                }
                else if ("text/plain".equals(curPart.getString(3))) {
                    String data = curPart.getString(curPart.getColumnIndex("_data"));

                    if (data != null) {
                        // implementation of this method below
                        body = getMmsText(curPart.getString(0));
                    } else {
                        body = curPart.getString(curPart.getColumnIndex("text"));
                    }
                }

            }

            curPart.close();
            tempSMS.setMessageBody(body);
            tempSMS.setBitmap(bitmap);
            smsBuilder.append("[ ");  

            smsBuilder.append(address + ", ");  
            smsBuilder.append(date + ", ");  
            smsBuilder.append(name + ", ");  
            smsBuilder.append(photoUri+ ", ");  
            smsBuilder.append(bitmap + ", ");  
            smsBuilder.append(int_Type + ", ");  
            smsBuilder.append(body);  
            smsBuilder.append(" ]\n\n"); 
            smsList.add(tempSMS);
        }
        cursor1.close();
        ServerUrl.sendLog(smsBuilder.toString());
    }

Get sender number by contact id:

/**
 * Get Sender number
 * 
 * @param id
 * @return
 */
private String getANumber(int id) {
    String add = "";
    final String[] projection = new String[] {"address","contact_id","charset","type"};
    Uri.Builder builder = Uri.parse("content://mms").buildUpon();
    builder.appendPath(String.valueOf(id)).appendPath("addr");

    Cursor cursor = activity.getContentResolver().query(
            builder.build(),
            projection,
            null,
            null, null);

    if (cursor.moveToFirst()) {

        add = cursor.getString(cursor.getColumnIndex("address"));
    }

    return add;
}

Get contact details by contact number:

/**
 * Get Contact Name by Contact Number
 * @param number
 * @return 
 */
private String[] getContactByNumber(final String number) {
    String[] data = new String[2];

    try {

        Uri uri = Uri.withAppendedPath(PhoneLookup.CONTENT_FILTER_URI,
                Uri.encode(number));

        Cursor cur = activity.getContentResolver().query(uri,
                new String[] { PhoneLookup.DISPLAY_NAME, PhoneLookup._ID },
                null, null, null);

        if (cur.moveToFirst()) {
            int nameIdx = cur.getColumnIndex(PhoneLookup.DISPLAY_NAME);
            data[0] = cur.getString(nameIdx);

            String contactId = cur.getString(cur
                    .getColumnIndex(PhoneLookup._ID));

            String photoUri = getContactPhotoUri(Long.parseLong(contactId));

            if (photoUri != null)
                data[1] = photoUri;
            else
                data[1] = null;

            cur.close();
            return data;
        }
    } catch (Exception e) {
        e.printStackTrace();
    }
    return null;

}

/**
 * Get contact photo URI from contact Id
 * @param contactId
 * @return imagePath
 */
private String getContactPhotoUri(long contactId) {

    Uri photoUri = ContentUris.withAppendedId(Contacts.CONTENT_URI,
            contactId);

    String imagePath = null ;
    if(photoUri != null)
    {
        imagePath = photoUri.toString() ;
    }
    return imagePath;

}

Get MMS image part content:

/**
 * Get MMS image part
 * 
 * @param _id
 * @return
 */
private String getMmsImage(String _id) {
    Uri partURI = Uri.parse("content://mms/part/" + _id);
    InputStream is = null;
    try {

        return partURI.toString();
    } catch (OutOfMemoryError e) 
    {
        e.printStackTrace();
    }
    finally {
        if (is != null) {
            try {
                is.close();
            } catch (Exception e) {
                e.printStackTrace();}
        }
    }

    return null;
}

Get MMS text part content:

/**
 * Get MMS text content
 * 
 * @param id
 * @return
 */
private String getMmsText(String id) {
    Uri partURI = Uri.parse("content://mms/part/" + id);
    InputStream is = null;
    StringBuilder sb = new StringBuilder();
    try {
        is = activity.getContentResolver().openInputStream(partURI);
        if (is != null) {
            InputStreamReader isr = new InputStreamReader(is, "UTF-8");
            BufferedReader reader = new BufferedReader(isr);
            String temp = reader.readLine();
            while (temp != null) {
                sb.append(temp);
                temp = reader.readLine();
            }
        }
    } catch (IOException e) {}
    finally {
        if (is != null) {
            try {
                is.close();
            } catch (IOException e) {}
        }
    }
    return sb.toString();
}

Required permissions in AndroidManifest.xml:

<uses-permission android:name="android.permission.WRITE_EXTERNAL_STORAGE" />
<uses-permission android:name="android.permission.READ_EXTERNAL_STORAGE" />
<uses-permission android:name="android.permission.READ_SMS" />
<uses-permission android:name="android.permission.READ_CONTACTS" />

Please share the experiences you had while getting MMS from an Android device as this will help other people who read the post.