Just my random thoughts.
1) To Boethiah the Fount of Inspiration.
It was on behalf of Boethiah that the Chimer followed Veloth.
2) To Hircine who is Half the Conscience of Man.
Hircine, the Huntsman, to human instinct, which is to survive. Hunting is the basis of any basic (long-term) survival.
3) To Malacath who speaks all Languages Sideways.
To speak sideways is to lie. Perhaps this could be attributed to the fact that he proclaims himself a Daedric Prince although the other Princes don't recognize him as such.
4) To Mehrunes Dagon whose mistress is Blazing Sun.
Fire, destruction.
5) To Sheogorath the Comforter of Men.
A mad man is a happy man.
8) To Mephala who threads the Needle with the Hair of wives.
Apparently her spheres are "obscured to mortals". But to thread the needle pretty much means to find a solution to an impasse. From Vivec and Mephala: "Mephala is understood paradoxically to contain and integrate these contradictory themes". I couldn't begin to guess what the Hair of wives part means, but the above quote would fit in perfectly with threading the needle.
9) To Clavicus Vile who always answers.
His sphere is granting wishes. Duh.
12) To Azura the Rim of all Holes.
Azura's spheres are dusk and dawn, the "Holes" between daylight and darkness?
14) To Hermaeus Mora who holds the Paper to the Light.
This is an attribute to hidden knowledge. There are several applicable meanings, such as seeing through the paper to see something else, or to see something within the paper.
16) To Vaermina Weaver of the Panoply.
A panoply is a protective covering, so perhaps this could be a reference to some sort of metaphorical membrane between real life and dreams.