The weird pig shown in the pictures will be called "Sowser"
A mixture of Sow- A word for pig (But isn't it a mother pig...?), and Bowser.
Sounds a little blunt since Bowser's going to be going against Sowser, but whatever.
Okay, so here's my attempt at the story from what we've found:
A strange disease strikes the Mushroom Kingdom, infecting Toad's and blowing them to huge sizes. Mario and Luigi go to Peach's Castle to attend a meeting on how to cure the disease. Suddenly, Bowser attacks, and Mario easily defeats him. Bowser's kicked out, into a forest, where he finds the Lucky Mushroom (Which is actually a trap set by Fawful) with a Magikoopa, which gives him the ability to suck in things like a vaccuum. Bowser goes back, and sucks in Mario, Peach, Luigi, a few Toad's (Including Toadbert), and Chippy (The Strange Yellow Star). Bowser procedes to go on a rampage, sucking in all the Toad's in the Kingdom. Mario and Luigi survive, and run around, helping people. Later, Bowser finds his castle being attacked, and a strange pig (Sowser) takes over. Somewhere in all this, Bowser finds Brirock and Blodog (the Block things) and PROBABLY sucks them in (A source states that Brirock helps Mario).
Other Details:
*Fawful also takes over Peach's Castle
*Fawful is Sowser's Boss
*It appears (as Fullmetal said) that Mario and Luigi will eventually escape Bowser and roam the land. They may even join Bowser in the end. The official Mario and Luigi site shows 3 bubbles, one with Bowser and one with mario and Luigi in Bowser, and the two bubbles pointing to a bubble with a ?, which is the end game (or middle game) gameplay.
I CAN'T WAIT!!!!