Dear Vikral,
a) I live in the hills.
b) I live on the hills.
c) I live on a hill.
d) I live in a hill.
In British English, not all of these would be regarded as �correct �.
a) "You live in the city. He lives in the country-side. She lives at the sea-side. I live in the hills". The region where I live has several geographical features. There is an area of my region which is �hilly � and has many hills, (which are not as large as mountains). My house, my home, is in that area, and that is where I live.
b) "I live on the hills". This would not normally be used. It implies that I �exist �, �I survive �, �I live � by eating and using the produce which I find living or growing on the sides of the hills in the hilly district. A soldier, a fugitive or a trapper who is �living rough � might use this phrase, but it is not usual.
c) "You live in a flat area. She lives in a valley. I live on a hill". My house is possibly on the side of a hill; or my street is not level, but is at an angle of (say) 30 degrees. When I go home, I must either walk �uphill � or walk �downhill � to reach my house.
d) "I live in a hill". Unless I am a rabbit, or an ant, or a burrowing animal or insect which lives underground, I would not use this expression. Except in very rare circumstances, human beings do not "live in a hill".
I hope that this helps.
Les
