Domus
The Domus was a house owned by rich Roman citizens. There was a front opening, and one could see all the way through a house to the rear garden. There would then be a shrine, and then a living room and a garden. On the sides of the house you would have private rooms, the kitchen, etc.
Villa
The Villa was a country house, usually owned by rich Roman who also owned a Domus. There was the Rustic Villa, with lots of farm work performed. There was also the normal Villa, which would usually have large gardens, maybe even with a diverted stream running through it. They would even be built in windy area’s to provide adequate airflow to the house.
Insula
The Insula was basically an apartment for poor people. The richer, middle class would live on the bottom floor with more comforts than the floors higher up. Oftentimes, each family would have one room with everything being performed in that room. There also would not be private bathrooms most of the time, and instead there would be public bathhouses nearby.