After further research I found some relevant functions. Keep in mind it's probably better to separate these into different functions, and if your WordPress theme gives you any trouble, check this out.
// disable url field
function disable_comment_url($fields) {
if(isset($fields['url']))
unset($fields['url']);
return $fields;
}
add_filter('comment_form_default_fields', 'disable_comment_url');
// disable email field
function disable_comment_email($fields) {
if(isset($fields['email']))
unset($fields['email']);
return $fields;
}
add_filter('comment_form_default_fields', 'disable_comment_email');
Also be sure to visit Settings >> Discussion and uncheck the "Comment author must fill name and email" option to avoid user comments being rejected upon submission.