'낡다' means 'to be old and become worn out' and it is only used for items not for a person. e.g. 신발이 낡았어요. 차가 낡았어요. '오래되다' means 'items or relationship have been long' and is used for items or time (duration). '오래되다' does not necessarily mean 'to be worn out' even if it is old if it is an item. e.g. 이 차는 오래됐어요. 저 집은 오래됐지만 깨끗하고 좋아요. 우리는 오래된 친구예요. (We are old friends.) - duration of the relationship *'늙다' is only used for a person or animals. However, it may sound offensive if you use it for a person. 그 남자는 아주 늙었어요. (The man is very old.) --> This may sound offensive (ageism). 그 고양이는 늙었지만 귀여워요. You can say "그 고양이는 나이가 많지만 귀여워요." instead and '나이가 많다 'sounds better than '늙다'. cf. 그분은 아주 연로하세요. (polite) : '연로하다 (to be aged,elderly)'