The Sword of St. George sidequest revolves around the use of a mysterious "Rusty Sword" item and using it in conjuction with resting with party members. A word of warning first, this sidequest includes copius amounts of resting with party members which may bring you over the 50 day limit, so it's advised that you use the Kira boss fight (accessed by writing "KIRA" in the Bizarre Memo obtainable in Japan) to reset the day back to 0 when this happens.
To first gain the Rusty Sword, one must be under Day 22 and have cleared 3 playthroughs or more. To start, fight Utah in Hong Kong, but not fight him at the Harbor. If you do so, you end up having to fight his zombified form, which ends up in his death. By avoiding the fight with him at the Harbor, you can meet him in Edfu and fight him for the item, which he mentions was given to him as a family heirloom long ago, by a man named George.
Next, add Kakyoin to your party and sleep until he asks if he can take a look at the sword. Answer "Yes" and an event will play out in which the sword absorbs his power becoming the Emerald Sword. Kakyoin suggests you should destroy the sword, but you should say no.
Add Polnareff to your party, and rest until he asks to look at the sword. The same thing will happen to him transforming the sword in to the Holy Emerald Sword and he will advise you destroy the sword. Again, do not.
Add Abdul to your party, rest, the same event will happen and the sword will become the Magic Emerald Sword. He will say to destroy the sword. Don't.
Add Joseph to your party, and the sword will absorb his Ripple turning it in to the Ghostly Emerald Sword. He will offer to buy the weapon from you for the Speedwagon Foundation. Decline his offer.
Add Kakyoin to your party, his Emerald Splash will be absorbed transforming the sword in to the Precious Emerald Sword. Say no when he says to destroy the sword.
Add Jotaro to your party, rest, his stand power will be absorbed turning the sword in to the Power Emerald Sword. Say no when he says to destroy the sword.
Iggy is next, but his event is phrased differently from the others, being that you are given the choice to stop him from touching the sword or not.
Say no, and the event will proceed, with the sword absorbing Iggy's power.
However, the power in the sword grows so great, that it ends up breaking.
This isn't the end of the event chain, however. One must then go to Emporio's Room and fight Ultimate Being Kars, who has a 25% of dropping the Red Stone of Aja. If he doesn't drop the item, it's heavily advised to reset so you can fight him again.
Once you have the Red Stone, stay in the hotel with Iggy again until an event triggers in which you are given the choice of Touching the Broken Sword and the Red Stone, or waiting.
Touch the Sword and Stone, and you will get the Sword of St. George!
The Sword itself is an incredibly powerful combat item that can be used an unlimited amount of times, and can easily turn the tides of battle in your favour.
Alternatively, if you don't have the Red Stone of Aja, you can trigger an event in which you obtain the Godly Emerald Sword.