In Let Me In, Why Abby thinks Owen not invite her in his house?
She started bleeding for not inviting her then Owen stops her by hugging her.
Why does she think like that ?
Because he specifically asks her what happens if he doesn't invite her in - when she walks in she is answering his question (i.e. she starts to bleed and generally appears to suffer).
When hugging her he explicitly invites her in which stops the bleeding and pain.