where to put php code for wordpress login

I’m trying to create a login system for my wordpress blog which uses the users google account info to login so they can leave comments and vote on posts and so on. I have the php code on how to do this with and it works when I use it as a static html page but don’t know where to add it in wordpress for it to work properly without errors, I tried to add it in the header.php but that doesn’t seem to be right and some errors are generated sometimes,

    <?php
//Googles API
require_once 'google-api-php-client/src/Google_Client.php';
require_once 'google-api-php-client/src/contrib/Google_Oauth2Service.php';

//start session
session_start();

$client = new Google_Client();
$client->setApplicationName("Google UserInfo PHP Starter Application");

// Visit https://code.google.com/apis/console?api=plus to generate your
// oauth2_client_id, oauth2_client_secret, and to register your oauth2_redirect_uri.
// $client->setClientId('insert_your_oauth2_client_id');
// $client->setClientSecret('insert_your_oauth2_client_secret');
// $client->setRedirectUri('insert_your_redirect_uri');
// $client->setDeveloperKey('insert_your_developer_key');

$client->setClientId('473410134519.apps.googleusercontent.com');
    $client->setClientSecret('******');
    $client->setRedirectUri('http://www.pharzan.com/bitlog');
    $client->setDeveloperKey('AIzaSyBLKLt******');
$oauth2 = new Google_Oauth2Service($client);

if (isset($_GET['code'])) {
  $client->authenticate($_GET['code']);
  $_SESSION['token'] = $client->getAccessToken();
  $redirect = 'http://' . $_SERVER['HTTP_HOST'] . $_SERVER['PHP_SELF'];
  header('Location: ' . filter_var($redirect, FILTER_SANITIZE_URL));
  return;
}

if (isset($_SESSION['token'])) {
 $client->setAccessToken($_SESSION['token']);
}

if (isset($_REQUEST['logout'])) {
  unset($_SESSION['token']);
  $client->revokeToken();
}

if ($client->getAccessToken()) {
  $user = $oauth2->userinfo->get();

  // These fields are currently filtered through the PHP sanitize filters.
  // See http://www.php.net/manual/en/filter.filters.sanitize.php
  $email = filter_var($user['email'], FILTER_SANITIZE_EMAIL);
  $img = filter_var($user['picture'], FILTER_VALIDATE_URL);
  $personMarkup = "$email<div><img src='$img?sz=50'></div>";
  $name=filter_var($user['given_name'], FILTER_SANITIZE_STRING);
        //Get user details if user is logged in

      $user_id              = $user['id'];
      $user_name            = filter_var($user['name'], FILTER_SANITIZE_SPECIAL_CHARS);
      $email                = filter_var($user['email'], FILTER_SANITIZE_EMAIL);
      $profile_url          = filter_var($user['link'], FILTER_VALIDATE_URL);
      $profile_image_url    = filter_var($user['picture'], FILTER_VALIDATE_URL);
      $personMarkup         = "$email<div><img src='$profile_image_url?sz=50'></div>";

  // The access token may have been updated lazily.
  $_SESSION['token'] = $client->getAccessToken();
} else {
  $authUrl = $client->createAuthUrl();
}
?>

then I need to use such code to display the user markup image and to see if they are logged in or not.

<?php if(isset($personMarkup)): ?>

    <img class='markup' src='<?php   echo $profile_image_url;?>'> </img>

<?php endif ?>

<?php //USER NOT LOGGED IN
  if(isset($authUrl)) {

   print "<a class='login' href='$authUrl' title="Login with google" </a> ";
   print "<script>console.log('.$authUrl.');</script>";
  } 
  else {
  print '<a class="log_out" href="?logout"> Logout?</a>';
  print "<script>console.log('.$authUrl.');</script>";
 }
?>

My problem is I don’t know where to include this code in wordpress,
If I put it in the header the first part gets loaded every time and produces errors on the
start_session() part and also if I need to process the information in different parts of the page, say once in the header and once in the footer I don’t know how to include the code.