Why is oblique case used here?
Because घर is followed by में, postpositions like में change how you refer to the noun into the oblique case.
Difference between hamara ;hamari;hamare and where to use them
हमारा: masculine singular. हमारे: masculine plural, oblique case, formal. हमारी: feminine.
Why hamare? And not hamari?
...because it qualifies "ghar" which happens to be in oblique case.