For the characters you are choosing to work with, pride would probably be the biggest single motivator. Immortals who are part of a very small group (which would seem smaller with every passing decade) would have an incredible hangup with status within that group. The pecking order would be so meticulously hammered out after a couple thousand years of these same people interacting that any kind of slight at all would probably set one of these guys off against another one.
In fact, given their immortality, it's safe to say that all of these characters would have been at war with all the other ones at one point or another in the past, and would probably end up both allying with and being opposed to every other one again in the future. This gets more interesting when you stop to think that several of them can predict the future to one extent or another, so they KNOW that they will be allied with the guy who is their arch enemy right now against their best friend right now in another millennia or so.
You indicate that they can get powers from one another. That right there is a big motivator. What is the process for getting a power away from another member of the pantheon? What benefits accrue to them other than the power itself? Is their social pecking order predicated on number of powers obtained? If not, you could end up with a super powerful character with tons of powers being constantly slighted. Not the most stable situation...
Immortals would be very weird characters. They would remember slights made against them centuries ago. In Greek mythology, these characters were petty, shallow, and very over the top in their reactions to one another. Part of that is because they were supposed to be archetypes. Even if they weren't so shallow, you have to figure it would get strange with the same 20 people interacting literally forever. You think you get tired of your co-workers in your office? Try living with them 24/7 for a few CENTURIES! I find it very believable that these guys would probably be pretty neurotic by our standards.
One thing they may be fighting over (and which may even act like currency among them) is the ability to forget! Think about it: if their brains don't degrade and they are immortal, the impacting layers of year after year after endless year of listening to Zeus' stupid puns and knowing you would listen to them for the rest of all eternity would LITERALLY drive you crazy. Whoever has the power to wipe away some clutter in the form of memories would be selling that as a party favor. Take some forget juice, wipe away a few centuries of the same old BS, and feel refreshed! They would also probably "become mortal" periodically in order to live a mortal life, forget stuff, die, and actually have some kind of a delineation in the endlessness of infinity which they would look at with almost dread.
How do you look forward to endless years exactly the same as the years you have already experienced? That doesn't seem like heaven so much as purgatory... Mortality itself might be a valuable gift. In this connection, if you wanted to explore that, you might look up On A Pale Horse by Piers Anthony, or one of it's numerous successors. In that universe, the "god" position had become kind of an office, which the current inhabitant of would inevitably grow very very tired of and find a way to off themselves, but since someone had to replace them for the universe to remain in balance, they usually had to find a willing or unwilling replacement. The details of this turnover make most of the plot of the series, which is extremely interesting.
To get back to your question: I think they would be trying to climb the ladder of power and replace the guy on top. Powers would be one tool in this game, as would divine and semi-divine progeny and allies. Some kind of system clearly would exist to displace the guy on top, since according to Greek Mythology Zeus himself did in order to set up the current pantheon. That seems to be the only place to go for a mid level Greek deity. There really isn't much potential for advancement in that job, come to think of it. Honestly, it might even be the big motivation for some deity-of-something-or-other to get OUT of being that and force some other shmuck to be stuck in that role for eternity. Remember the stories of Hades, stuck underground and unable to be with his love during the times she was above?
If you think this through, these guys sound a lot more like eternal bureaucratic functionaries than rock stars, and even rock stars get tired of THEIR jobs after enough decades of partying. If I were doing this: I would make them unable to STOP being a deity-of-whatever without a specific writ from mr. Big Boss and unable to really permanently die either unless they get that. That creates a huge motivation: getting OUT of the prison of being stuck with the same 20 people doing the same thing for all of eternity!