Custom form not showing in correct place on page

When working with shortcode you must return a value rather than output directly. The below amendmetn should fix your positioning issue.

For more informaiont, see the Shortcode API Codex, speciffically the Output section.

function multipage_form()
{
    global $wpdb;
    $this_page      =   $_SERVER['REQUEST_URI'];
    $page           =   $_POST['page'];
    if ( $page == NULL ) {

        /**
         * first name
         * last name
         * email address
         * current job title
         * // autofill with linkedin //
         */

        // output form
        $my_form = '<form method="post" action="' . $this_page .'">

            <label for="FNAME" id="FNAME">First Name:</label>
            <input type="text" name="FNAME" id="FNAME" required="required" />

            <label for="LNAME" id="LNAME">Last Name:</label>
            <input type="text" name="LNAME" id="LNAME" required="required" />

            <label for="EMAIL" id="EMAIL">Email address: </label>
            <input type="text" name="EMAIL" id="EMAIL" required="required" />

            <label for="CURRENTJOBTITLE" id="CURRENTJOBTITLE">Current Job Title:</label>
            <input type="text" name="CURRENTJOBTITLE" id="CURRENTJOBTITLE" />

            <!-- Hidden value for page -->
            <input type="hidden" value="1" name="page" />

            <input type="submit" value="Next" />

        </form>';
    }   // END PAGE 1 FORM

    elseif ( $page == 1 ) {

        // store POST variables
        $first_name         = $_POST['FNAME'];
        $last_name          = $_POST['LNAME'];
        $email              = $_POST['EMAIL'];
        $current_jobtitle   = $_POST['CURRENTJOBTITLE'];

        // get taxonomy terms
        $years_experiences = get_taxonomy_terms('job_listing_category');
        $job_types = get_taxonomy_terms('job_listing_type');
        $job_regions = get_taxonomy_terms('job_listing_region');
        $job_tags = get_taxonomy_terms('job_listing_tag');

        /**
         * are you (freelancer, ...)
         * you live in (brussel, ...)
         * years of experience
         * expertise in digital (choose max 2: data science, e-commerce, ...)
         */

        // output form
        $my_form.= '<form action="' . $this_page .'" method="post">

            <label for="JOBTYPE" id="JOBTYPE">Are you...</label>
            <select name="JOBTYPE" id="JOBTYPE">
            ';
            foreach($job_types as $job_type)
            {
                $my_form.= '<option value="' . $job_type->term_id . '">' . $job_type->name . '</option>';
            }

            $my_form.= '</select>

            <label for="JOBREGION" id="JOBREGION">You live in...</label>
            <select name="JOBREGION" id="JOBREGION">
            ';
            foreach($job_regions as $job_region)
            {
                $my_form.= '<option value="' . $job_region->term_id . '">' . $job_region->name . '</option>';
            }

            $my_form.= '</select>

            <label for="YEARSEXPERIENCE" id="YEARSEXPERIENCE">Years of experience in digital:</label>
            <select name="YEARSEXPERIENCE" id="YEARSEXPERIENCE">
            ';
            foreach($years_experiences as $years_experience)
            {
                $my_form.= '<option value="' . $years_experience->term_id . '">' . $years_experience->name . '</option>';
            }

            $my_form.= '</select>

            <p>Expertise(s) in digital (choose maximum 2):</p>';

            foreach($job_tags as $job_tag)
            {
                $my_form.= '<input class="single-checkbox" type="checkbox" name="tags" value="' . $job_tag->term_id . '">' . $job_tag->name . '<br>';
            }

            // Hidden value for page
            $my_form.= '<input type="hidden" name="page" value="2" />
            <input type="hidden" name="form_id" value="' . /*$form_id*/ "hello" . '" />

            <input type="submit" value="Submit" />

            ';
    }   // END PAGE 2 FORM

    return $my_form;

}