tordi

No -ord- suffix, and no suffix of any kind. The word is tord- plus the infinitive -i, full stop. Esperanto has no -ord-, and the run of borrowed words that end that way - ordo, ordinara, akordo, rekordo - share nothing but a Latin accident. What makes this seam tempting is that ordo is a real Esperanto root meaning order, and t- looks like nothing much, so the eye offers you a parse. Refuse it. One root.

Transitive, so watch the -iĝ-. Tordi takes an object: you twist something. The thing that twists by itself is tordiĝi. Mi tordis la ŝnuron against la ŝnuro tordiĝis, and if you get that pair right you have the whole igi/iĝi system in miniature. The same applies to an ankle: mi tordis al mi la piedon is how the sprain is normally said.

Against turni. Turni is rotation about an axis - a key, a head, a wheel. Tordi is deformation: you are changing the shape of the thing, wringing it, wrenching it out of true. A cloth full of water is tordata, not turnata. Figuratively tordi does the same work English gives to twisting the facts, and tordita of a face is contorted.