1To smell good; to be fragrant — used of flowers, perfume, food, etc. giving off a pleasant scent. Written with 匂う in this sense. In everyday speech, the noun form 「いい匂いがする」 is more common; the verb 匂う has a somewhat literary or descriptive feel.
庭の梅の花がほんのり匂う朝だった。
It was a morning when the plum blossoms in the garden were faintly fragrant.
お母さんからは、いつも石鹸がやさしく匂っていた。
My mother always carried the gentle scent of soap.
焼きたてのパンがオーブンから甘く匂ってきた。
The sweet smell of freshly baked bread came wafting from the oven.
2To stink; to give off a bad or unpleasant smell — used for garbage, sweat, drains, and other foul odors. Written with 臭う in this sense. Extremely common in everyday speech, e.g., 「なんか臭うね」 "something smells" or 「これ臭ってない?」 "doesn't this stink?".
夏場のゴミ箱は本当に臭う。
The trash can really stinks in the summer.
ねえ、なんかちょっと臭わない?
Hey, doesn't it smell a little?
排水溝が詰まっているのか、台所が臭ってきた。
Maybe the drain is clogged — the kitchen has started to smell.
運動した後の体操服がひどく臭う。
My gym clothes reek after exercising.
3To glow; to seem faintly bright or richly colored. A literary/classical usage describing how flowers, sunsets, skin, etc. seem to shine or take on a beautiful hue. Almost never used in modern everyday speech — mostly encountered in waka, haiku, and classical-style writing.
夕日に山々が赤く匂っていた。
The mountains glowed red in the setting sun.
桜花、匂うがごとく咲き満てり。
The cherry blossoms bloomed as if glowing in full splendor.
4To smack of something; to give off a hint or whiff of something — used figuratively to suggest that something suspicious, fishy, or characteristic seems to be present. Colloquially used like 「なんか匂うな」 to flag a suspicious feeling. The noun form 「〜の匂いがする」 is more common.
この話、なんか匂うな。裏がありそうだ。
Something about this story smells off — there's probably more going on behind the scenes.
彼の証言には嘘が匂う。
His testimony reeks of lies.