I've found yet another word that's translated as 'home' which now makes it 3. Could you please tell me if these words have the same exact meaning or is there any difference between their usage?
1 Answer
家屋 and 家 can mean the same thing. However, 家 more often than not implies your own home, while 家屋 does not have this implication. Also, 家屋 has as special meaning when talking about local real estate tax ([固定資産税]{こていしさんぜい}), were it probably is most often used. In this situation it pretty much means any building with a roof on it, including factories or warehouses, etc.
住居 can be thought of differently than 家屋 or 家, as it does not necessarily refer to a house, it can be thought of as "the place where one lives". For example, many people live in apartments, etc. and this also can be consider one's 住居.
Note there are many other similar words, 住処、自宅、住宅、住まい、etc.