(An example of a house made by me. /\) Houses can be made from anything except crimson/corruption blocks and pearlstone/pearlsand blocks.
I made 10 out of the 14 of my houses completely out of mushroom and it works fine.
A tip in making houses would be to:
1.Get 60 walls of anything (not corruption/crimson/pearl/dirt walls).
2.Cover the walls with blocks of the type the wall is from.
3.Get a chair and table (or work bench) and place them close to each other, without space.
Put a torch in a corner of the house.
Put the door on one of the sides.
It says on the site that the house must have at least 60 blocks, counting the walls too. It must also be 42 or more blocks away from corruption/crimson or hallow, so putting the blocks from those biomes will cause the house to become invalid.
A good way to "save" space would be to build the houses on top of each other. Be sure you put blocks so the NPC's can get in the houses. Putting Rope is enough. Make sure to put them on both sides of you hadn't acquired the Ice Mirror or other home-teleporting items.
Hope it helps you as much as it helped me. A lot.