These three expressions have almost the same sound. Nevertheless, they have different meanings.
There is used in the expressions There is and There are or as an adverb of position. There is/There are means Il y a in French, Es gibt in German, C'è/Ci sono in Italian, Hay in Spanish. Er is/Er zijn in Dutch. E.g.: There is a boss called Pegasus. NOT Their is a boss called Pegasus or They're is a boss called Pegasus.
Their is the possessive adjective/pronoun of they. Like I→my, you→your, he→his etc. E.g.: Desmond and Go'fer live in Frostburn. Their house is in Frostburn. NOT There house is in Frostburn or They're house is in Frostburn.
They're is the contractive form of They are. Like I am→I'm, you are→you're, he is→he's. E.g.: Desmond and Go'fer are dwarves. They're dwarves. NOT Their dwarves or There dwarves