These two episodes (and probably the rest of the season I suspect) deal the overall story arc of the series, which is Sam & Dean's missing father and what happened the night their mom died.
In "Home" Sam reveals that he might be psychic when he has a dream of a lady in their old childhood home screaming for help. So they go back and find out the house is being haunted by a poltergeist. They also try to get to the bottom of their father's dissaperance by asking around and finding out he became friends with a local psychic.
The psychic tells them that if they plant some mystical stuff in the house, the poltergeists (How odd that yesterday I said the one episode resembled "Poltergeist") will vanish. While putting the mystical stuff, the poltergeists attack which results in trashing the house. When the owner comes back, she seems pretty ok with the damage. But they get the mystical stuff in place and all is well.
Except not. The flame ghost thing appears and it's about to kill Sam when (Spoiler alert) the ghost of their mom appears to do battle! Unfortuately we don't see the battle, but in the end, the poltergeist is gone for good and Sam & Dean go on their way.
When the psychic goes back to her crib, Sam & Dean's dad is sitting there! It's not made clear if he's alive or dead, but if he's alive, won't they feel stupid for not checking out their old hometown first? And this episodes most fucked up moment was when a plumber came (at night for some reason) and we see him unplug the garbage disposal so he can stick his hand down the drain. Guess what happens next.
"Aslyum" reminded me of that old MTV show "Fear" where they'd put 5 people in some spooky haunted place and they had to investigate spooky rooms and spooky stuff would happen and I keep saying the word spooky over and over again. Spooky. Anyway, Sam & Dean get a text message from their Dad to check out the aslyum. Sam don't want to but Dean insists on following orders.
At the aslyum, they find out the doctor in charge, back in the day, would use the mental patients as guinea pigs for his weird experiments. The inmates rioted and killed the doctor, and the place got shut down. I never understood why there are even abondoned buildings. If a place closes down, why isn't it knocked down right away? I always found that weird.
Anyway, like I said, this episode is more about backstory then the ghost and we find out that Sam resents Dean for always being in charge and always doing what their dad tells them to do and crap like that. And when the ghost doctor gets ahold of Sam, he makes him mental and attack Dean, who then knocks him out. A quick burning of the doctors dead body and Sam is back to normal, which is hiding the fact he secretly hates Dean.
The episode ends with Dad calling and Sam picking up the phone. Oooh! Cliffhanger!