Sometimes she is considered to be to be associated with/a Fomorian, but usually she is of the Tuatha De Danann.
She is the wife of battle, or the god of battle Neit. *(Although she is not directly called a god she is seemingly always listed with gods and goddesses and has many characteristics of a god.)
The Morrigan is not only associated with Crows and Ravens—though crow is her more usual form, she is also able to change into an eel, a heifer and her calf, and a wolf bitch.
The Morrigan is not only an Irish goddess, there are carrion crow battle goddesses evident in archealogical discoveries across the continent as well with Gaulish inscriptions to her under a similar name to Babd.
The Morrigan is a mother. She has three sons, and two still-born twins a brother and sister.
The Irish associated the Morrigan with Lilith, in a 9th century Irish translation and gloss of the Bible, they referred to Lilith as a Lamia, a female monster, that is a Morrigan.
There are caves and pairs of hills resembling breasts named after the Morrigan and one of her names Anu in Ireland.
The Morrigan can be a very large woman, able to have one leg on either side of a river.
The Morrigan does shape shift she is seen variously as a beautiful fairy young woman, an old hag, and of course as a mother as mentioned above. She is most often depicted as three sisters. Despite that, the mother maiden crone set up is still probably an ill fit because she is not associated with the moon directly—and is not a creatrix goddess. And besides that she has many more forms than just those three.