By default, if used within ordinary paragraphs in org mode, M-up and M-down transpose *lines* (not sentences). This was not useful to me. The following code makes these keys transpose paragraphs, keeping the point at the start of the moved paragraph. Behaviour in tables and headings is unaffected. It would be easy to modify this to transpose sentences.
(defun org-transpose-paragraphs (arg) (interactive) (when (and (not (or (org-at-table-p) (org-on-heading-p) (org-at-item-p))) (thing-at-point 'sentence)) (transpose-paragraphs arg) (backward-paragraph) (re-search-forward "[[:graph:]]") (goto-char (match-beginning 0)) t)) (add-to-list 'org-metaup-hook (lambda () (interactive) (org-transpose-paragraphs -1))) (add-to-list 'org-metadown-hook (lambda () (interactive) (org-transpose-paragraphs 1)))