EAUC = Enlisted Aircrew Undergraduate College, I think. It's that basic aircrew training at Lackland, they teach you basics of how aircraft function, systems, weights arms and moments, stuff like that. Some will be easy as a wrench-turner, but it's also an introduction into the math you'll be doing in BBOC/BLM, among other things. I can't speak too much about it since I didn't have to go.
Booms deal a little less with pax since refueling is their primary mission, but there are plenty of -135s and -10s running around with pax and cargo onboard. For the -135s there were entire Guard units on orders for a long time flying the airborne cattlecars, the "135 rotator" moving crews from one end of the system to the other, seemed they didn't do any A/R at all. KC-10s, being at such obvious hubs in the AMC system, seems they'll always have ORF space-A's tagging along whenever they go somewhere (except Al Dhafra), plus they can carry a bunch of pallets so they tend to do that too...so yeah, booms deal with pax and cargo too.
I can't speak too much about boom stuff since I'm *not* a boom, but there's plenty of booms around here to answer that stuff.