Acoustic measure of a specific room
Tricky problem. Any speaker to mic path in a room is actually a linear time invariant system so they can be fully described by impulse response or transfer function. However the transfer functions are very complicated (1000s of degrees of freedom) and vary tremendously with position in the room. The room is also a very effective de-correlator. Signals from the same speaker recorded at two different location will seem mostly uncorrelated. 

You could try to use some statistical room acoustical properties: diffuse field power, reverb time, early decay time, reflection density, mean free path lengths etc. However, these are difficult to determine and not that much different between most rooms in the same house. 

So unless you can deploy some significant constraints (control the excitation, control location of source and microphone), this will be very hard to do.