Once you've entered the Strange House, you'll notice that where you go is determined by where the furniture in the house feels like sitting. If it's blocking an area, you can't explore it. If it's moved out of the road, feel free to go right ahead and enter the door or go down the steps.
Luckily, this doesn't happen at random, so you can use a methodical approach to explore the house. First, go west and descend the stairs leading down to the basement.
Strange House B1F
Move east through this decrepit library. You'll notice that you can grab a Spell Tag ; do so. Continue east. You won't be able to grab the other item here just yet, so ascend the stairs at the east end.
Strange House 1F
You'll notice the door to your west is now open. Go through it. Inside is a poor Backpacker, assumedly having been stuck in this house for quite a while. Poor dude! Move up to him to have him challenge you.
Trainer Battle: Backpacker
Once he's been defeated, exit the room and head to the very eastern side of the main room. Move up the staircase here and follow the path around until you stop and the ghost of a girl appears. She'll disappear soon after appearing.
Now head west and down the staircase on the west side. Move around the furniture and enter the door just to the west of the main staircase in the centre of the room. Grab the Full Heal inside. Now go back down the stairs to your west, down into the basement once more.
Strange House B1F
It's a bit more of a maze in here than it was before, but you can now get the second item. Head to the northern wall first, then head east along it. Move between two of the blue chairs and continue east to the sofa facing east. Move down the left side of it and head west between two of the bookshelves.
When you reach the blue chairs again, head down to the south wall of the basement and head east. At the end you'll find the Dusk Stone . Pick it up, then head back to the sofa. Move back to the north wall and head east to the eastern end. From there, move south down to the stairs. Ascend the stairs when you're ready.
Strange House 1F
Now head up the eastern staircase of the main room. Follow the path along to the first door. Enter it. Move to the north-east corner of this room and grab the Rare Candy . Exit the room back to the main area. Head back down the eastern staircase and head all the way across the room to the western staircase.
Move up them and enter the door at the top. Inside is a female Psychic. Walk up and talk to her to start a battle.
Trainer Battle: Psychic
Once she's defeated, exit the room and head down the western staircase and up the central one. The ghost will appear again and disappear once more. Head north and enter the door there. The room inside is all nice and new, which is rather odd.
It's the ghost's room and she seems to have some crazy obssession with keeping her room tidy. Ghosts these days. Shakes head Anyway, there's an item on the rug here. Move up and grab it, a Lunar Wing ! Yes! The ghost will appear behind you and shock you. She'll say a few words before disappearing for the last time.
The Lunar Wing can be used later on to encounter Cresselia on Marvelous Bridge . The Pokemon League will need to have been conquered before you can even access the bridge though, so it's going to be a fair while before you can put it to good use.
Anyway, exit the Strange House and continue following on from where you left off.