I think he is given a wooden sword and has to fight demons and things like that.
He is not used to the 20th century since he was dead for a long time. He then lives with this girl he saved when he first got out of hell. He also is followed by a guy from hell who watches him to make sure he doesn't do anything bad.
I remember one part where there is a bank robbery and he defeats all the robbers and saves everyone in the bank also most of the people have demons in them he has to defeat
It's Togari. It's about a boy named Tobei who has been dead and living in hell for over 300 years.
Summary:
He tried to escape hell multiple times but got caught repeatedly. One day he was made an offer that if he could kill 108 demons in 108 days, then he would be free to return to Earth.
He agrees on doing this and then gets sent into modern-day Japan.
Things that definitely match your description:
On the cover you can see his magical sword that can easily be mistaken with a wooden sword or stick.
He lives together with a girl name Itsuki Asagi. He saved her from getting raped and murdered by a thug. After this, they live together with her grandfather.
In volume 3 they are caught in the middle of a bank robbery with one of the bandits holding Itsuki hostage.
