Allow HTML in Custom Metabox area

I fixed your input type/sanitization and escaping issues. I think there's still some cleanup that could be done with this code though. I see inputs without labels, invalid attributes, etc.

add_action( 'add_meta_boxes_post', function ( $post ) {
    if ( $post->_wp_page_template === 'page-templates/skyscraper-post.php' ) {
        add_meta_box( 'sky_post_excerpt', 'SkyScraper Post Excerpt and Links', 'sky_post_excerpts', 'post', 'advanced', 'high' );
    }
});
add_action( 'save_post', 'post_meta_box_save' );
function sky_post_excerpts() {
    global $post;
    $values = get_post_custom( $post->ID );

    $strong_title = isset( $values['skyscraper_strong'] ) ? stripslashes(wp_filter_post_kses(addslashes( $values['skyscraper_strong'][0] ) ) ) : "";
    $title = isset( $values['skyscraper_post_title'] ) ? esc_attr( $values['skyscraper_post_title'][0] ) : "";
    $text = isset( $values['skyscraper_post'] ) ? esc_attr( $values['skyscraper_post'][0] ) : "";
    $image = isset( $values['skyscraper_post_image'] ) ? esc_attr( $values['skyscraper_post_image'][0] ) : "";

    // We'll use this nonce field later on when saving.
    wp_nonce_field( 'my_post_meta_box_nonce', 'post_meta_box_nonce' );
    ?>

    <table class="form-table">
        <tbody>
        <tr valign="top">
            <th scope="row">
                <label><strong>Skyscraper Title</strong></label>
            </th>
            <td>
                <p><textarea class="widefat" rows="4" name="skyscraper_strong" id="skyscraper_strong" ><?php echo $strong_title; ?></textarea>
                </p>
                <p><input class="widefat" rows="4" name="skyscraper_post_title" id="skyscraper_post_title" value="<?php echo $title; ?>"/>
                </p>
            </td>
        </tr>

        <tr valign="top">
            <th scope="row">
                <label for="skyscraper_post"><strong>Skyscraper Page Excerpt</strong></label>
            </th>
            <td>
                <p><textarea class="widefat" rows="4" name="skyscraper_post" id="skyscraper_post"> <?php echo $text; ?></textarea>
                </p>
            </td>
        </tr>
        <tr valign="top">
            <th scope="row">
                <label for="skyscraper_image"><strong>SVG Image Link</strong></label>
            </th>
            <td>
                <p><input class="widefat" rows="4" name="skyscraper_post_image" id="skyscraper_post_image" value="<?php echo $image; ?>"/>
                </p>
            </td>
        </tr>

        </tbody>
    </table>
    <?php
}


function post_meta_box_save( $post_id ) {
    // Bail if we're doing an auto save
    if( defined( 'DOING_AUTOSAVE' ) && DOING_AUTOSAVE ) return;

    // if our nonce isn't there, or we can't verify it, bail
    if( !isset( $_POST['post_meta_box_nonce'] ) || !wp_verify_nonce( $_POST['post_meta_box_nonce'], 'my_post_meta_box_nonce' ) ) return;

    // if our current user can't edit this post, bail
    if( !current_user_can( 'edit_post' ) ) return;
    $allowed = wp_kses_allowed_html();

    // Make sure your data is set before trying to save it
    if( isset( $_POST['skyscraper_post'] ) )
        update_post_meta( $post_id, 'skyscraper_post', wp_kses( $_POST['skyscraper_post'], $allowed ) );

    // Make sure your data is set before trying to save it
    if( isset( $_POST['skyscraper_post_image'] ) )
        update_post_meta( $post_id, 'skyscraper_post_image', wp_kses( $_POST['skyscraper_post_image'], $allowed ) );

    // Make sure your data is set before trying to save it
    if( isset( $_POST['skyscraper_strong'] ) )
        update_post_meta( $post_id, 'skyscraper_strong', wp_kses( $_POST['skyscraper_strong'], $allowed ) );

    // Make sure your data is set before trying to save it
    if( isset( $_POST['skyscraper_post_title'] ) )
        update_post_meta( $post_id, 'skyscraper_post_title', wp_kses( $_POST['skyscraper_post_title'], $allowed ) );
}