You can store any kind of seafood in the freezer if it meat is solid, like shrimp, lobster, fish, squid, oyster, and clams without cooked or steamed. But not crab and Mantis shrimp.
To store oysters you can either open the oysters and clean them or leave them as it is and clean them later, and if you decide to clean them and then place them back on the half-shell and cover it up with the other half-shell to make the whole oyster and tie it with a rubber band or kitchen string and put them all in the bag so it’s won’t stick together when you take them out from the freezer.

Fisherman

First of all, buy fresh oysters or clams to make sure 1, They are displayed in the water, not on the ice, 2, making sure that the shell is closed, and if the shell opened even a little gap, just touch them with your finger. If they react to that and close it quickly that means it’s still alive and if not close it’s dead, you don’t know how long it has been dead.
here’s another piece of advice, if run into any kind of crabs that are on sale and you can’t say no to it and you want to buy a lot of lbs. and want to store some for later on. Don’t freeze them while they are still alive, you must steam them before you freeze them. Crab meat is not solid meat like shrimp. If you freeze before steamed you will have nothing to eat from the crab after you take it from your freezer.