How do they relieve stridor in tracheostomy patient?

Trach solves: Stridor is essentially noisy breathing. Usually a tracheotomy bypasses the problem. If the person still has stridor with a trach, as the questioner asks, then there is blockage in the trach. Mucus plug, trach is too small, collapse, granuloma, etc are all common causes of tracheal obstruction. This is not usually called stridor however. The questioner may really be asking why trachs work?

Depends: Usually stridor is due to blockage of the upper airway. If the patient has a tracheostomy, there should be no blockage. Unless of course if the patient is trying to talk around the tracheostomy, in which case stridor may be due to narrowing of the airway between the larynx (voice box) and the tracheostomy tube.