Weird, odd, and strange are often synonyms and can usually be used interchangeably. Of these three, "odd" is sometimes used differently. In the phrase "odd one out" odd doesn't just mean something that is unusual/weird/strange, it means something that is different than the others in the group. I would not really consider "rare" a synonym for the others. Something that is rare is unusual and uncommon, or not often found. Rarity often, but not always, implies value. There are "rare" gemstones, "rare" events and "rare opportunities" and all of these are good/exciting things.