I know that many of the lesser Aedra sacrificed themselves in the creation of the mortal universe and I know that the Eight Divines gave up some of their power to maintain it, but how much do they have now? None have truly shown themselves in the world so far...the altars and shrines could be enchanted to do what they do.
I'm not even sure of the appearance of the Avatar of Akatosh would count as intervention/appearance since even that required Martin Septim to sacrifice himself. Only Sithis and the Daedra make themselves known and the Tribunal were more powerful than the Divines...so...do the Divines truly have power?
Another, somewhat related question: if we play as the Dovahkiin, the first that's known to have appeared since Tiber Septim, how could Martin (or ANY bearing the Septim name) have been adequate to light the Dragonfires/become the Avatar?
They created Nirn, so yes they are real. The divines are the very reason the planet exists in the first place. There is plenty of prove for that. Just follow Morrowinds MQ to completion if you have doubts. Talos is also a divine. Just see http://uesp.net/wiki/Oblivion:Blood_of_the_Divines
To make it as short as possible:
Back before there was Nirn, Lorkhan/Shor (name depends on culture) tricked/persuaded (depends on culture) the other Aedra (the 8 you see in game, plus some more) to create a mortal world. They did, one guy called Magnus was the architect of the world but fled before it's creation was complete because he realized the toll it would take on the spirits building it, his fleeing ripped a hole in the sky (the sun) which now allows for magic on Nirn (Tamriel + other continents)
After this the remaining spirits became the earthbones (planet) and were probably really pissed at Lorkhan so they ripped the heart out of his body and shot it away (landed in Red Mountain, Morrowind).
The Aedra are thus the creators of the planet. The Daedra are simply spirits like the Aedra were, who decided not to join Lorkhan in making the planet. They are what Aedra were before.
The Tribunal are gods that one day found and used the Heart of Lorkhan to get their divine power (as did Dagoth Ur) their strenght thus comes from a dead god. Which is why, when the hearts enchantments that bind it to the Tribunal are destroyed they also lose divine power, which is why you can kill Dagoth Ur, Vivec and Almalexia and why Almalexia could kill Sotha Sil.
Tiber Septim became an Aedra by doing exactly what Lorkhan did only with creating an Empire instead of a planet and thus appeared close enough to Lorkhan and the creation myths to be mistaken as Lorkhan (walk like a god, talk like a god, etc.). He and two others rose up to the "heavens" and became the ninth divine. Basically he takes Lorkhan/Shor his place in the temple.
As for the dragonblood things, the Septims after Tiber all had dragonblood, whether they had this by birth or simply got it by becoming Emperor is unknown. Fact remains that they did have dragonblood.