Hi. Scream is used to describe loud cry of a person as a rule. She scraemed with a horror when saw what she did. Screech is likely to relate to any mechanisms. The car' brakes screached terribly from huge strain but that saved driver's life.
I guess shriek is similar to word scream and could be usd either person or any tools and apparatuses. The shriek of a cargoship reminds us with
Fandorin has done a good job trying to differentiate. I would add onloy that a shriek is probably a shorter scream and that it is no coincidence that it rhymes with eek, a word that some people would say when they suddenly see a mouse.