Despite the augment's claim that you only need to have sex with men and women 15 times each, they must all be different people, hence the term "Swinging".
To achieve the "Swinger" augmentation in single-player and without building a Brothel, you must have access to the Mercenary Camp and the Bowerstone Old Quarter. In the Mercenary Camp, find the two whores, interact with them and hit the corresponding button for the sex invite (sometimes it is not available right away so keep trying until you get it). Do not hold hands with either of them, but rather fast travel to the Old Quarter (they will still follow you) and find the other two whores, initiate the sex invite for them as well, and take your group to the next bed available.
Once the "Swinger" augmentation has been unlocked, this weapon has the highest base damage of any sword in the game.
The "Singing Sword" mentioned in the description refers to a cancelled quest in Fable where you would help a bard and receive a weapon called The Singing Sword. The quest card from the quest was left in the data of the Fable discs.
The Swinging Sword is part of a small group of weapons that are extremely rare. It is only 'common' in the Sanctuary's riddle chest and the 50 silver key chest in Bowerstone Castle's garden.