When Zee Tamil or Kalaignar TV broadcasted the film, they hired professional dubbing artists. Om’s character—both the 1970s junior artist and the modern-day superstar Om Kapoor—was voiced by an artist who imitated SRK’s signature baritone but added a local lilt. Deepika’s character, Shantipriya/Sandy, was given a soft, classical Tamil dubbing, preserving her ethereal beauty.
If you are looking for a movie actually filmed in Tamil, there is a 2015 supernatural drama with this exact name. Om Shanti Om Movie Tamil Dubbed