Hmmm ... you could either go with Imperials as race (Zeus = Jupiter, Poseidon = Neptune, Hades = Pluto), since they're based off the Romans who had tight connections with the Greek, or you can choose a race with overlapping attributes. For example, an Argonian for Poseidon, since they can breathe under water. Oh yeah, and make sure you're male in all three instances.
For Zeus, you could become Dragonborn, since dragons are aspects of the sky in the TES universe. And a Nord for that matter, as they are called the Children of the Sky. Clear Skies and Call Storm shouts may be your main shouts. If you're on pc, you could always use the tcl command to pretend you're levitating, or you could literally become a dragon via commands (by taking over the controls of a dragon you meet, but I don't remember the commands anymore). He not only governs the sky, but also thunder, so you might go with shock magic. Also, your house should be somewhere high atop a mountain, like Mount Hrothgar (among the greybeards?). And he's someone who chases after the ladies. ^^ He's got a certain affinity with goats too, seeing as he's been raised by one for a while.
As I already mentioned before, Poseidon could be an Argonian for its waterbreathing ability. He uses a trident, but the closest thing I can think of is the fork weapon you can get on the balcony of Honeyside.

He's been called the "tamer of horses", and has a close association with horses. Drowning a horse is a sacrifice to him, to calm the sea (so if you encounter dead horses in the water, know someone has made a sacrifice for you! ^^). Poseidon is said to cause some types of mental disturbance, e.g. epilepsy (you could make some sort of link to Sheogorath if you wish). Poseidon actually possessed a house in a settlement next to the sea (Solitude springs to mind).
As Hades, you could maybe become a vampire (and be an undead, but I don't know ...). Only race I can think of in the TES universe are Dwemer, since they're the elves from the Deep, but they're pretty much gone. :/ On the matter of weapons, he uses a bident (absolutely no idea what could refer to that), and a helm/cap of invisibility. Hades is also called "the unseen", so invisibility is important. Another artifact of his is the three-headed dog, so go find one!

Also, the other undead shouldn't be roaming the living plane, but your plane (he gets very angry when they try to leave his plane), so you could go for the elimination of all the wandering undead (kinda like Meridia actually, her sword Dawnbreaker might be useful there). Also, he hates when souls get stolen, so he should be against soul capturing. He also gets furious when people try to cheat death or stand in his way. Hades is after balance however, and thus neutral instead of evil as people often see him as nowadays. He might be cruel and pittiless, but just. Hades governs the underworld, and with it, all the riches in the ground (i.e. ores). he's a rich guy in other words. Oh yeah, just a head's up, but Hades
rules over the death, and is not Death itself (that's Thanatos). Black animals are sacrifices to him, and human sacrifices are quite a big no-no. During winter, Hades is together with his wife Persephone (I dunno, maybe you could get a wife to follow you whenever you travel through snowy terrain?). His home is misty and gloomy, and full of dead of course. Oh, and there's a ferryman to bring the dead to his realm, but I don't know whether you can implement that somewhere.
Hope this helps.