There are differences, it's just not easy to describe...
Ein Ort can mean a small town. It can also mean a geographical location.
Ein Platz can mean a plaza. It can also mean a designated area or a seat, often with a possessive pronoun: "mein Platz" = my seat/ my chair/ my space.
Stelle is a very small defined spot. It's where you lost your necklace or where they found the body. You can point to the ground and say "right here, das ist die Stelle". "Platz" would sound too big for this, unless you want to say "das ist der Platz, wo meine Kette immer lag" (That's the spot where my necklace used to be), implying the necklace has a designated spot of it's own.
"Stelle" is also used for "job", like "Ich habe die Stelle in der Verwaltung bekommen" = "I got the job in administration".