Given that Skyrim is having a rise lately around me, I thought I'd have a read up on it again. This topic has always been interesting, and I certainly hope I'm not shunned for continuing this thread. ESPECIALLY, since it is full of delicious content and reasoning.
Firstly - Herma Mora. The Daedric Prince of Knowledge and Fate may have power at his disposal, but you need to realize that his knowledge has a limit. The knowledge itself is power, because the information leads to great power by whatever means. Whether it be a dreadful secret that can bend the knee of those scared of blackmail, or whether it be the secret to a blade that can destroy any foe. This can be applied to the OTHER Daedric Princes. They have great power, and with the way things are, there is potential for there to be Knowledge behind how that power works. Herma-Mora may seek this knowledge out, but he'd undoubtedly never get it. A Daedric Prince would not likely surrender the key to their own power, so Herma-Mora wouldn't be able to do much in the straight up combat against another Prince, unless he just HAPPENS to have a decent sum of natural power himself.
In the topic of Herma-Mora's artifacts being powerful; that's actually not the case. The artifacts themselves are powerful because they are extensions of his knowledge being granted to Mortals. It isn't exactly powerful when compared to a Daedric Prince. For example - he granted the power to control Dragons to Miraak and the Last Dragonborn. A Dragon isn't exactly a threat to a Daedric Prince, though.
Of course - Azura has her power, which I'll leave to the earlier discussions.
Boethiah, I can mention having great influence over the real world by the brief events of Skyrim. After a ritual that the Dragonborn partakes in, by killing a follower, Boethiah begins jumping from body to body to conversate with the Dragonborn. This form of possession only seemed valid with dead bodies, but it was nevertheless a sudden influence that definitely made the average first player jump in their boots. I've not got much knowledge on this myself however, so I'll leave Boethiah out of my idea.
Molag Bal can be comparable to the above. During the House of Horrors quest, when you attempt to make Logrolf the Willful (I think) submit to the Daedric Prince, you end up killing him. Molag Bal simply laughs, and proceeds to resurrect Logrolf in front of the Dragonborns eyes. However, this could greatly be an ability that most Daedric Princes possess, but both Molag Bal and Boethiah tend to show it off more (Another reason for their rivalry). With this, and given the nature of the Mace of Molag Bal, it can be seen that he has great influence over the world. I'd imagine that the concept of the Mace is normally that the Soul Trap effect is supposed to send Souls to Molag Bals realm, Cold Harbour, but I've not checked up on this sort of thing. Like before, I've not got too much more to say on this.
Clavicus, Peryite, Meridia, etc. Rely entirely on Mortals for their purpose, so yknow. Not that impressive at first glance. You could certainly try to find reasonings on them being more powerful that one thinks however, considering that Clavicus has the ability to grant Mortals items upon bargaining. The extent of this ability is unknown to me. Meridia is likely to be unrelenting against something like Molag Bal, as previously mentioned, due to her hatred of the Undead. His creation of Vampires is likely disgusting to her, but her power is unsure of still. Peryite has the responsibility of order among the lesser Daedra, but this could be an advantage one wouldn't firstly think about. He may have the vaster army, though it could still be considerably weaker. His influence is also pretty wide, considering he is known for spreading disease. A side thought that I had, though without evidence admittingly, is that he could have potentially influenced both Hircine and Molag Bal. Given the nature of Sanguine Vampiris and Sanies Lupinus, there is potential that Peryite gave cause for less pure versions of Molag Bal and Hircine's creations, as they became a spreadable disease. This could boast that he was able to interupt their own power, but it could also just be that they didn't care enough to stop him. Plausible thought, though?
Mehrunes Dagon appears to be quite the brash type, powerful, but forgetful of preparation. Even if he is incredibly powerful, he weakens himself whenever breaking into Nirn, and doesn't ever give himself the time to recuperate before he is beaten. I wouldn't be too fast on saying that he is the most powerful of the Princes, though. Same as before, I don't know much on this. The Oblivion Crisis isn't exactly something he'd have had to do alone though, but more he was the Daedric Prince that took the first bite. I've not double checked this, but I'm correct to think that other Daedra took advantage of the situation too? So with that mind, using the Oblivion Crisis as an example of his powerscaling isn't entirely accurate if I'm right.
I'm not even going to get into Jyggalag. I personally dislike the whole process of that. I'd have rather Sheogorath just been Sheogorath, and that's that. However, Sheogorath in mind, I'm glad to know that he's not just immediately overpowered over the other Princes. The 16 Accords of Madness is a gift to the Elder Scrolls Lore in my honest opinion. Everything said above about Sheogorath and the 16 Accords of Madness not using actual power is my reasoning.
I hear alot about Mephala supposedly being very powerful, can't even remember what information I saw that made me think of them as such. I remember reading somewhere that they are potentially the Dark Brotherhood's Night Mother herself, or the Night Mother is an extension of her. This links her to Sithis, which has some potential power increases on her behalf. However - I have no evidence of such, and influence from Sithis may not count towards the Daedric Princes power in this forum. It can also be noticed that Mephala actually has more interest in Mortals, than displaying their own power. Lies, deceit, sex, etc. That's all the good stuff for Mephala. I get the vibe that their power mainly comes from seduction, assuming they could ever seduce another Daedric Prince. (I've seen too much hentai to see where this is going with Herma Mora. D:)
Someone like Namira doesn't seem like they'd be all that powerful, as they just like yucky things. They could wiggle their moldy toes at the Daedric Princes, but would likely be defeated by Neloth if they used such a technique. :)
Now, seeing an earlier topic about who gets dibs on a soul, I'd assume that it really depends on the choices made by the Dragonborn. I'd say that Molag Bal and Hircine get first dibs, assuming that the Dragonborn is either a Vampire or a Werewolf. I'm unsure if a Vampires death leads to them being claimed by Molag Bal, but I'd certainly assume so. If not, then Hircine takes the pickings. If the Dragonborn is a Nightingale, but also a Werewolf, I would certainly expect that such a physical curse would take the lead.Hircine would get dibs over Nocturnal. Oaths can be broken, business contracts can be made null and void, but a curse is unwillingly given, or at least unable to be broken by just saying 'meh'. Of course - it could always lead to a stalemate, and whichever Prince is more powerful would get dibs, assuming they cared enough. It could also be based off the severity of the binding. A Nightingale has a responsibility of protecting Nocturnals Twighlight Sepulcher, whereas a Werewolf/Lycanthrope joins a Hunt in Hircines realm. The Nightingale has more resting on their shoulders, so it can potentially be a case of some background agreements between Princes, on who's soul binding has greater value. Again, it can be up to contest over a valuable soul like the Dragonborns.
Realistically, taking a look at the Princes, I would consider the most powerful being based off of their influence on the world. Jyggalag might be powerful, but he doesn't really do anything other than being powerful. Mephala is busy whispering lies and desires into peoples minds, and Hircine and Molag Bals unnatural diseases run rampant throughout Tamriel. Molag Bals creations were prepared to blot out the sun itself, and Hircine's Werewolves just kill and kill without thought. Malacath has the entire Orc race based around him, and is even recognized by Dark Elves. Mehrunes Dagon is feared for his actions during the Oblivion Crisis, and Nocturnal decides whether a Thief is able to pickpocket someone or not in a specific moment. This can be seen plenty, and I definitely think that the better question would be about what Princes actually have validity in Nirn.
My final answer on who is most powerful? I'd have to personally say that the straight up strongest would be Mehrunes Dagon. In a 1v1 fight, I'd imagine that his role would allow for him to win such a fight. Based on the types of armies they have though, I'd imagine something like Mephala's Spider Daedra comprised army would be pretty strong, but one must also remember just how potentially strong Hircines army could be. We are talking about a realm stuffed full of all the dead Lycanthropes. Werewolves are particularly powerful creatures, and shouldn't be taken lightly. Herma-Mora's army of seekers, behind the tanky Lurkers, could be a real threat too. The poison that the Lurkers spread is actually deadly, as I remember having to hold down my healing spell for a long time to survive a blast from it. The seekers appear to be gifted in magic that most Daedra wouldn't know either, so it implies that they are gifted with the Knowledge that Herma-Mora has to offer, which does make them exceptionally powerful in the way he makes mere mortals become gods among themselves.
That's all I have to say, not once backed up with evidence, but I feel like it is fair? Cheers for reading.