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Literally "dog god" is not really a god but a spirit that can be either helpful or malicious. It may be summoned in a number of ways, but usually the torture of a living dog is involved. The spirit may be kept by a family for protection but it could also possess humans and cause trouble.
The name either means "entangling bride" or "whore spider", which both insinuate what she does. She is based on the japanese golden orb-weaver spider and preys on men by turning into a beautiful woman.
There are a few different versions of the hashihime legend. Tn one she's a woman who's been thrown out by her unfaithful husband, and so she prays to become an oni in order to torment him. The gods tell her to perform a ritual for 21 days under a bridge, commonly the Uji bridge, hence the name which means "bridge princess". Her name is also a homophone for "pretty princess" in old japanese and she may previously have been associated with a completely different myth.
The name kasha actually means "fire cart" and it isn't clear when it became a monsterous cat, but throughout history it's believed to steal away the body during funerals.