All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad (saw) is His slave and Messenger.

If these cats and dogs really cause much harm and disturb people as to cause their life to become miserable, then it becomes permissible to kill them. However, one should first try his best to get rid of them by any way without killing them, such as by transporting them away and terrifying them by hitting them slightly… etc.

Perhaps you could also consider moving elsewhere.

Allah knows best. (Source: islam_web) Classified in Foods, Drinks, Clothes and Adornment > Hunting