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What happened to Hermione’s clothing and other possessions after she wiped her parents’ memories of her? And what about those empty picture frames?

Note: This answer refers to the Book only; the movie had aspects not found in the stories

Nothing; they are likely still in her closet / dresser / etc. Her parents picked up and moved to Australia. If her parents owned their home (not unlikely) and Hermione took the time to think things thru and prepare (quite likely, given that this is, after all, Hermione), their home is probably mothballed and waiting for them to come home.

She did take the time to plan this out, charm her parents, and pack ("for days"), so I can't see her not having taken precautions with regards to their home and her possessions.

Her picture is still in all of the frames; the pictures are just still back at the house.

“Let’s see,” said Hermione, slamming Travels with Trolls onto the
discarded pile with a rather fierce look. “I’ve been packing for days,
so we’re ready to leave at a moment’s notice, which for your
information has included doing some pretty difficult magic, not to
mention smuggling Mad-Eye’s whole stock of Polyjuice Potion right
under Ron’s mum’s nose.

“I’ve also modified my parents’ memories so
that they’re convinced they’re really called Wendell and Monica
Wilkins, and that their life’s ambition is to move to Australia, which
they have now done. That’s to make it more difficult for Voldemort to
track them down and interrogate them about me—or you, because
unfortunately, I’ve told them quite a bit about you.

“Assuming I
survive our hunt for the Horcruxes, I’ll find Mum and Dad and lift the
enchantment. If I don’t—well, I think I’ve cast a good enough charm to
keep them safe and happy. Wendell and Monica Wilkins don’t know that
they’ve got a daughter, you see.”

The movie script indicates that as well as modifying her parent's memories, magic also took care of the evidence of her physical existence in the house.

Note that from Hermione's perspective, her image is disappearing from the photo frames.

HERMIONE: Obliviate.

Mrs. Granger’s face goes briefly slack and she reaches

out, as if to break a fall, then, slowly, her hand drops,

coming to rest upon her husband’s. He blinks once,

blankly, and then... enfolds her fingers in his.
Hermione lowers her arm and, eyes stinging with tears,

watches the PHOTOGRAPHS placed about the room begin to

CHANGE. One by one, Hermione DISAPPEARS from each.

In the novel we don't learn what happened to her personal effects but we do know that Hermione is perfectly capable of using magic to make objects fly, transfigure and disappear.