Ajax call returns 0 when add_action is inside a class in functions.php

While I am not sure why you want to do it like this, please find below the working code. Please note the comments in line. I hope this helps.

class test{
    public function __construct() {
        add_action( 'wp_ajax_test2', array( $this, 'test2' ) );
        /* Front end ajax needs this. */
        add_action( 'wp_ajax_nopriv_test2', array( $this, 'test2' ) );
        add_action( 'wp_enqueue_scripts', array( $this, 'test1' ) );
    }

    public function test1() {
      /* in JavaScript, object properties are accessed as ajax_object.ajax_url, ajax_object.we_value */
      wp_localize_script('test-script-ajax', 'ajaxobj', array('ajaxurl' => admin_url('admin-ajax.php')));
      /* Moved your js to a separate js file and enquing it the WordPress way */ 
      wp_enqueue_script( 'test-script-ajax', get_stylesheet_directory_uri() . '/js/test-ajax.js', array( 'jquery' ));
    }

    public function test2(){
        echo "success";
        exit;
    }
}

$ob_call = new test;
$ob_call->test1();

Here is the code in test-ajax.js file

jQuery(document).ready(function($){
  var data = { 'action':'test2' };
  jQuery.post( ajaxobj.ajaxurl, data, function( response ) {
            alert(response);
    });
});