The incidents occurred in between Thane and Mumbra railway stations on the suburban Central Line of the Central Railway.
65-year-old Ram Ozare and a 35-year-old unidentified woman died while crossing railway tracks near Mumbra, an official with Government Railway Police (GRP), Thane said.
Another unidentified man was killed when he fell off a running suburban train, he said.
Two persons - Anwar Hussain Shaikh (35) and S K Mouz (25) sustained serious injuries after they fell off a running suburban train between Mumbra and Kalwa stations, the officer added.
Cases of accidental deaths have been registered in this regard, police said.