A giant mushroom that has a sliding door like from Star Trek that has the Homestar logo on it.
You really don't see much of it.
Has a cow lamp in it. (Broken by The Cheat during StrongBadEmail/caper)

In 'The Reddest Radish,' it looks like this:

'The Reddest Radish' has an animation style which is deliberately less sophisticated than most other toons.

A few notes:
1) In StrongBadEmail/caper, Homestar's living room looks bigger than the whole mushroom does in The Reddest Radish and In Search of the Yello Dello. On top of this, we see him walking out of a completely different-looking house in The Best Decemberween Ever. Could Homestar have moved since The Reddest Radish? That was marzipan's house.
2) It was The Cheat who broke the cow lamp, not Strong Bad.
3) Added picture of the interior.

In The new yello dello it was square but still had spots.

In The Best Decemberween Ever, the house that Homestar walks out of is supposed to be a spoof off of Charlie Brown, (along with his hat and the brick wall.) Homestar is supposed to be Charlie Brown and Strong Sad is supposed to be Linus, (although they should switch those two characters.)

That house is know marzipan's because she was in it in 3 times halloween funjob

Maybe Homestar had a sleepover with Marzipan....