I've grown up in North India and have never word anyone speak the word "avashya" outside of a Hindi lesson. I can only assume your grandmother was using it as an exemplar for your benefit. Perhaps there are communities where it is spoken colloquially but by far the norm is "zaroor" or "jaroor" (same word but the sound has shifted in some places like Western UP from Z to J).

You can find examples of the use of "avashya" in the movies of Hrishikesh Mukherjee (like Golmaal and Chupke-Chupke) in which off-beat characters who made a special point of speaking the purest Hindi as part of their characters' eccentricity used "avashya" and other words like it, while the other characters who spoke normal Hindi didn't.