The house-burning down happened WELL before most of the events in the plot.
They visited Winry for maintenance after Scar's attack on them; after the 5th Lab, she comes to visit them, since Ed's hospitalized at the time (and she feels guilty over botching the former repair, forgetting a missing screw).
They go to Dublith to see if their teacher knows anything about how they can get their bodies back, and then learn she transmuted her dead baby son. Then Greed gets involved, only to be found out by King Bradley, the homunculus Wrath (though I'm not entirely sure how he learned of the Devil's Nest outside of deus ex machina, but whatever).
Then they meet Ling and his body guards Lan Fan and Fu. They travel back to Central to learn of Maes Hughes' murder, and mope around a while until Maria Ross is convicted, without a trial, of said murder. Ed acts as witness to her "death" at Roy Mustang's hands. The two get split up at Mustang's orders, letting Ed learn that Maria Ross lives; she and Fu leave the plot for a good while. Al winds up involved in Roy's investigation into the homunculi, which culminates in Lust's death and Jean Havoc's paraplegia. Ed meets his father, Van Hohenheim, who in his vast wisdom (even if he hides it behind a somewhat dopey demeanor - one that didn't really carry over to the anime until later on) sparks Ed's investigation into whether human transmutation of dead beings is even possible, which, in the end, proves to be negative - it can't be done. However, since Ed was able to pull Al's soul from the Truth, he suddenly realizes that this mean's Al's body must also still be alive, and thus it must be possible to bring him back.