The morphing between man and beast seems always associated with Hircine. His quest in Oblivion had to do with hunting a unicorn protected by half-man half-bull men. Harpies are found on his realm on ESO.
Now on Hagravens, well, yes they are associated with Hircine and revere him as one of the "Old Gods" much like some Reachman clan revere Namira or Molag Bal. We encounter hagravens who once were witches of Glenmoril in Solstheim. They were probably seduced by power and longevity and thus turned themselves into hagravens. While the Glenmoril Wyrd worship and respect Hircine in nature and offer cures, Hagravens and the Reachmen gravitate toward Hircine's more feral side. The simplistic yet untamed animal savagery.
Hagravens seem to worship more "evil" Daedric Princes.
There are tons of ES material that links Hagravens to Hircine.

And yet I am, and live—like vapours tossed.
I long for scenes where man hath never trod
A place where woman never smiled or wept
There to abide with my Creator, God,
And sleep as I in childhood sweetly slept,
Untroubling and untroubled where I lie
The grass below—above the vaulted sky.”