It's best to put these in a shell script:

#!/bin/sh
echo "This program will update blahblahblah..."
echo "After starting this program, enter your database password for root"
DATABASENAME=wordpress

mysql -u root -p <<-ENDMARKER

 use ${DATABASENAME};
 UPDATE wp_posts SET post_content = replace(post_content, 'http://oldurl.com/image/image1.jpg',  http://newurl.com/image/image1.jpg'); 
 UPDATE wp_posts SET post_content = replace(postcontent, 'http://oldurl.com/image/image2.jpg', http://newurl.com/image/image2.jpg');
 UPDATE wp_posts SET post_content = replace(post_content, 'http://oldurl.com/image/image3.jpg', http://newurl.com/image/image3.jpg');
 commit;

ENDMARKER

Make the script file executable after saving. The script method is better than using the pipe method so you can debug the script in stages, or later expand on it when you have more junk you need to cleanup.

Because you mentioned WordPress, I will provide a PHP-specific answer:

<?php
$mysqli = new mysqli("example.com", "user", "password", "database");
if ($mysqli->connect_errno) {
    echo "Failed to connect to MySQL: (" . $mysqli->connect_errno . ") " . $mysqli->connect_error;
}

if (!$mysqli->query("DROP TABLE IF EXISTS test") || !$mysqli->query("CREATE TABLE test(id INT)")) {
    echo "Table creation failed: (" . $mysqli->errno . ") " . $mysqli->error;
}

$sql = "SELECT COUNT(*) AS _num FROM test; ";
$sql.= "INSERT INTO test(id) VALUES (1); ";
$sql.= "SELECT COUNT(*) AS _num FROM test; ";

if (!$mysqli->multi_query($sql)) {
    echo "Multi query failed: (" . $mysqli->errno . ") " . $mysqli->error;
}

do {
    if ($res = $mysqli->store_result()) {
        var_dump($res->fetch_all(MYSQLI_ASSOC));
        $res->free();
    }
} while ($mysqli->more_results() && $mysqli->next_result());
?>

Example of PHP's mysqli-multi-query()

See:
http://php.net/manual/en/mysqli.quickstart.multiple-statement.php
http://php.net/manual/en/mysqli.multi-query.php