This is the complete story of the diamonds as far as I know:
1. Guy puts them into cake mix in the openinig sequence of GTA 4 (presumabley to smuggle them off the ship)
2. Same guy sells the diamonds to Gay Tony and The Lost attempt to ambush the exchange
3. The Ancellotti guys realise whats about to go down and Gay Tony gives the diamonds to his boyfriend so he can make a getaway. (Tony then flees with Luis Lopez in a seperate limo)
4. Johnny shoots down Tony's boyfriend's Limo and steals the diamonds
5. Johnny hides the diamonds in trash bags
6. Niko collects them from the trash bags that Johnny left them in earlier and gives them to Ray Boccino (who told Johnny to get them from the exchange).
7. Ray becomes suspicious that one of the guys who helped Niko to retreive the diamonds from the trashbags tried to rip him of by stealing some of the diamonds in order to sell them to make money for himself. He orders Niko to kill him and his buddies and retrieve the stolen diamonds
8. Niko and Johnny go to a deal with the Jewish Mob (Isaac and Mori etc) at The Libertonian. Just as the deal is about to take place, Luis shoots two of the Jews with an AK47 through the window of the museam. He then gains posession of the diamonds although we don't know how... Yet
9. Luis then gives the diamonds to Gay Tony
10. Some time later Niko and the McRearys kidnap Tony's good friend Gracie Ancellotti in order to use her as a bargaining tool to get the diamonds
11. The deal is set up and an exchange (gracie for the diamonds) takes place at a plant on Charge Island but just as is about to happen, Ray Bulgarin (who is thought to be the original owner of the diamonds) ambushes the deal and one of his men takes the diamonds and escapes up onto a nearby catwalk in the plant forcing Niko and Packie to fight it out with bulgarin's men in order to get them back. After much loss of life and destruction, Niko and Packie eventually corner The henceman that took the diamonds and point their guns at him. The henchman then throws the diamonds into the back of a passing garbage truck because he rightly believes that he will be shot dead even if he hands them over. This is the last we physically see of the diamonds
12. A couple of days later it is mentioned on a radio news report that a Homeless guy found the diamonds said to be worth $2 million and lives a happily ever after.
And yes it is very like Snatch. In fact I think GTA 4 is turning out to be very like a Guy Ritchie/Quentin Tarentino movie with all the different plot twists and interconnecting stories. It's quite good though... I like it