Nabe parties and Barbecue parties.
Japan has a big restaurant industry with all kind of cuisines of the world, besides many good 24 hour options of packaged food from convenience stores, bento shops and super markets. More over as Japanese homes, especially in Tokyo, tend to be small, home parties are not so common and people tend to eat out more. Getting invited to a home party in Japan is indeed a sign of very close friendship and respect.
A common form of home party is Nabe party where fresh vegetable, meat and various food items are boiled in a pot of hot water put on the center table. And a common sight is of everyone sitting on the floor around the pot and eating and drinking in a very cozy atmosphere. Chopsticks come very handy in this set up!
Many expats/foreigners in central Tokyo tend to have bigger homes with bigger more western style home parties where people bring some food or drinks along or in some cases cooked at the home. New condominium buildings tend to have common party rooms for the tenants which are quite large for big parties, a common sight there is kids' birthday parties. Barbecue parties are also quite popular at homes with large enough balconies or a garden.