In this strip I count at least four people plus Snoopy himself going into the Doghouse. There is even room for one more, though the house isn't so big. How do they all fit?
I'm not sure there's a physically correct answer. There are many aspects of "Peanuts" that don't make sense, but are there for the sake of comedy. If you are going to ask how so many people can fit into his doghouse, shouldn't you also ask how a dog can type (in English, I might add), or even how Snoopy is able to comfortably lay on top of his doghouse if the roof comes to a point? Half of the comics featuring Snoopy should have you asking "how is that possible?".
But that's what makes Peanuts so good. The strip is popular for its quaint humor and running gags, such as Lucy pulling away the football, or Charlie Brown always getting disrobed by line drives, not as much for its knee-slapping jokes. The size and quality of the inside of Snoopy's doghouse is no different than the latter two examples, except it isn't used quite as many times throughout the running of the strip. The idea that a tiny doghouse can have a recreation room, fit a pool table, and house many other items (including a Van Gogh painting) is ludicrous; that's what makes that particular strip funny. Below are a few other examples of strips that use the same gag of Snoopy's doghouse being bigger than it seems:
I suppose if one were to absolutely refuse to accept the humor of the situation, and demand a logical answer, it could be rationalized that the entire premise of Peanuts is similar to that of Calvin and Hobbes. That is, you never quite know what is reality and what is happening in the imagination of the children involved. This is often the case for Snoopy, as he is constantly fantasizing about fighting the Red Baron, or being in other action-packed situations, but we know that these are all in his head by the way the kids in the strip interact with him while he is wrapped up in one of these charades. It could be that his doghouse is normal sized, but the kids all want to make him feel better and so they participate in his illusions of owning a recreation room, pool table, etc, by squeezing into it and pretending to be impressed.
Overall, I think that the space inside of Snoopy's doghouse is supposed to remain a mystery, as it allowed Charles Schultz to give Snoopy whatever materials he needed for his next fantasy or adventure. Most comic strips take creative liberties, and I think that Snoopy's doghouse is just another silly gag that's funny purely because of the implausibility of it all. I mean, come on... how could a dog own a Van Gogh?