Many eyeball lights are battery powered (examples include AA and AAA cells and small LR44 demo cells). Some string lights use battery packs, while larger inflatables and blowers plug into AC power. A few plug-in pieces or inflatables specify they don’t require batteries.
Sizes vary by type: small tabletop or door-hanger props are typically under about 9 inches; yard stakes are around 26 inches tall; inflatables are roughly 3 ft (about 35.5 inches); string-light sets range from a few feet of lit length up to roughly 32.66 feet overall.