When I got rabbits as an adult, one of my big initial concerns was how to avoid fly-strike, heh - When I was 8 or 9, I had a rabbit who got a cut on his shoulder while running around the back yard and then got fly-strike in the wound as a result! Fortunately, I had awesome parents who rushed him to an after-hours vet as soon as we discovered it and he was able to be nursed back to heath, but the experience definitely stuck with me. If he's an inside bunny, I wouldn't worry too much though (especially this time of year when stray flies getting indoors are so uncommon). It never hurts to check his bootie daily, either - if caught early, fly-strike IS treatable.
As far as cleaning him goes, Blue eyes gave great advice. Rabbits should NEVER be bathed, as it can cause them to go into (fatal) shock... but a plastic shoe-box or dishpan with half an inch to an inch of warm soapy water (Dawn or other similarly animal-friendly soap is a good choice) to soak just their bottom can loosen up the poop. If you have to resort to cutting some of it out with scissors, rabbits have extremely thin and sensitive skin so it's extra important not to cut close to the skin!
A question about his bum - does the poop stuck to him smell at all? If it doesn't, then he's having runnyish fecal poops (ie diarrhea)... in that case, it's potentially from the stress of going to a new home and I would recommend small animal probiotics (like Bene-bac; available at some feed stores/pet stores and from some vets) and keeping a close eye on things as he may well require a vet visit. If it DOES smell (especially if it seriously stinks!), then it's cecal poops (ie cecotrophs).
Fecal poop is normally hard, round, odorless balls... up to 500 a day per rabbit, heh. Cecal poop is smeary, sticky and stinky but under normal conditions, you'd never know it exists because healthy adult rabbits ingest it directly from their anus so that it can pass through their digestive tract and get more nutrients sucked out of it. The two most common causes of cecal poop NOT being eaten are a) age - very young bunnies sometimes just ADD and don't bother eating it for whatever reason; this tends to remedy itself as they get a little older and b) too many pellets - too rich a diet (usually because of too many pellets) causes them to produce more cecal poop than they actually need to eat... hence, they leave the extras lying around. In your case, it's possible that he's leaving extras around and then sitting on them.
While the general rule of thumb is to let very young bunnies have unlimited pellets in addition to unlimited hay, if extra cecal poop is causing issues for your bunny then you should gradually cut back on pellets until the problem subsides. If you're still having issues, you could always try transitioning to an adult (timothy-based) pellet.
