If you're familiar with the
fucking weird as hell comic, Gunshow, then you might have heard of the series The Anime Club. If not, it's about four teenaged boys who are in a club devoted to anime. There are only a few "episodes" and it can get kind of NSFW at times [small](prime example: Part One: Mort Brings Porn to the Library)[/small] but I still recommend it. The guy's other stuff... well, just be warned. It can get pretty weird.
The Anime Club
There's also Blank It, which is about two guys trapped on a blank but constantly randomizing plane of existence. Updates are pretty slow, but there's about a few hundred pages worth of stuff, so there's enough to keep you occupied for a while.
Blank It
Next we have Gone with the Blast Wave. It's a shame, really, because the guy doesn't really like making the comics, but they're really funny and well written. It's about two soldiers who were separated from their squad in a post apocalyptic city.
Gone with the Blast Wave
Nextly, we have Moe. Okay, I know you wanted something a little more story driven, and Moe has some story, but it's a comic that goes under the radar for a lot of people and I really wish they would check it out. Moe is a loser. He's dumb, he's crappy at socializing, and he has the shittiest luck. But he pulls through, with his kid brother Bo. At first, it doesn't seem like there's a real story. It's just random comics about Moe in ever changing environments. And it's true. Still, there's still some story arcs that are really entertaining to read. Plus, it has a sense of humor that I find to be very different from anything else I have seen! Check it out.
Moe
Lastly, there's Rice Boy. Again, this doesn't fully fit your criteria, as it isn't very humorous. But I figured that it would make up for less of the story than Moe. Well, really, it's more of the world that's interesting. Rice Boy is sort of hard to explain... mainly because I forgot the story. That's because the story is actually pretty forgettable. However, it's a very fantasy heavy world. It has you just wanting to see what's next because the world is so fantastic. By the way, when I say very fantasy heavy, I mean "not ripping off Tolkien this time." Again, the story isn't the greatest feature.
However, the writer has written another story, Order of Tales [small](which is kind of "meh")[/small], and is in the middle of writing another [small](which is actually fantastic, in my opinion)[/small]. The latter, which I recommend more than Rice Boy and Order of Tales, is Vattu. It's about a tribal girl who gets sold into slavery. It's very dark and mature and I love every bit of it!
Rice Boy
Order of Tales
Vattu
There's all of the web comics that [small](mostly[/small] fit into your criteria. If you check them out, please tell me what you think of them.
[small](I just want to know if my tastes are on par with everyone else's. <_<)[/small]