Stink bugs do not lay eggs in the crevices of woodwork and make their way in as tiny nymphs, nor do they reproduce once they get in—mating and multiplying are warm-weather, outdoor activities. They (and their partners in crime, boxelder bugs and Asian lady beetles) slip in as full-grown adults when the first chill hits, to take advantage of the central heating. Making themselves as flat as stink bugs can, they crawl in through cracks in siding and window frames, or through an attic vent. If there's an opening, they'll find it.
Once inside, stink bugs don't eat anything, and they don't bite. They'll invade dresser drawers, park themselves on drapes, or find a comfortable spot on a toothbrush, but apart from bedding down in annoying places, and a little foolhardy buzzing when they can't remember their way out, stink bugs are perfect guests. Well, there is the smell...but you'd stink too if someone squished you.
Caulk is the answer. If you have an all-out stinkbug invasion, a professional energy audit will help locate every little crack and cranny. But not now—wait until summer. By then, assuming they've escaped detection, the bugs will have marched outdoors through the same cracks that gained them entrance, and they'll be happily mating, laying eggs, and nibbling on garden plants.
See how a New Jersey man made his own stink bug trap.