I do feel a little out of my league when people are talking about sources and stuff. The only 4th edition sources I have are the three core rule books. Even with those books I don't feel like I have a strong grasp of the mechanics of it.
Mastery of the system will come with practice; no worries. But with only the three core books, I think 354b is going to be hard-to-impossible to replicate exactly. Your best option is to reflavor one of the classes (warlock or wizard) as "psionic" (the fey warlock works well for this, though it adds a bunch of teleporting; the star pact warlock can work as well). Alternative, create a new character and bring in 354b later when there are options better suited to him.
Is the Blood of Vol religion an actual religion? I mean, is there any actual divinity going on there? Would a Seeker cleric or paladin make any sense? What would such characters pray to/get their power from? Themselves?
Yes, it is an actual religion. The key thing to remember is that in Eberron, no one has every met a deity. If their are deities running around, they are so distant so as to be non-existant. The only faith that has a tangible representation of their faith are the followers of the Silver Flame—the Flame itself manifests in Flamekeep—and the Elves of Arenal, whom can talk to their preserved ancestors that make up the Undying Court.
Seekers, however, take their faith internally. They believe power comes from within. Thus, they worship that idea and doctrine. A paladin of the Blood of Vol does not pray to a deity in that sense, they recite catechisms and other tenants of the Seekers, reaffirming their belief and preparing for a new day. A battle prayer would be a similar turn on these mantras, or a declaration of the enemy's misuse of their innate power.
Seekers believe the divine power does come from some innate power within themselves (thats the central tenant of their faith). Flamists believe their power comes from the Flame. The Arenal and Valenar elves believe that divine power comes from the reverence of their ancestors. Academics have no idea where divine power comes from, but they have several theories.
Key thing to note about Eberron: There are many questions. Very few have definitive answers.
Also, how long ago was the Last War?
pathfinderq1's got the right of it; the Treaty of Thronehold ended the war about 2 years ago. The Day of Mourning (the frightening arcane destruction of all of the nation of Cyre) happened four years ago; while fighting did not stop immediately, it curtailed soon afterwards.
The current year is 998 YK (years after the founding of the Kingdom of Galifar (the kingdom that existed before the Last War shattered them into five and more).