These weapons are remnants from the United States' war with China, an event that triggered the Great War. They were most likely brought back by American soldiers fighting in various campaigns in mainland China, or were brought by Chinese infiltrators and saboteurs like the ones at Mama Dolce's and elsewhere throughout the United States.
With its high durability and fast attack speed, the Chinese officer's sword is an excellent weapon outside of V.A.T.S., whereas swings in V.A.T.S. use 28 AP.
Vampire's Edge - The weakest of the Chinese officer's sword variants, Vampire's Edge weighs only one pound, and is the only variant to use the regular sword's skin.
Jingwei's shockswordOperation: Anchorage (add-on)- An electrified version of the Chinese officer's sword, the shocksword is much stronger and deals electrical damage over time.
Sim version Operation: Anchorage (add-on) - A version of the weapon which appears only within the Anchorage simulation. Unlike other sim-specific weapons, this version has a higher base and critical damage than its normal counterpart, and also causes disintegration for non-player characters killed by a critical hit similar to Jingwei's shocksword. This weapon is only carried by non-player characters within the Anchorage simulation and cannot be obtained through normal means.
Samurai's swordMothership Zeta (add-on) - An ancient weapon from Japan that deals an extra helping of damage on critical hits, and is much more durable than the standard sword.
The following is based on Fallout 3 cut content and has not been confirmed by canon sources.
In Fallout: New Vegas, an enlarged unusable version of the Chinese officer's sword can be seen behind elder McNamara's desk. It is part of a large Brotherhood of Steel symbol which consists of a sword offset from two interlocking gears.