Are shrimp, crabs, and oysters safe to eat after a hurricane or typhoon, as the storm might have stirred up all the sediment?

Bacteria: Your concern is bacteria. If the shell fish get washed ashore then you may have an issue. If when the water settles and the shell fish remain in their habitat and are then caught you should be alright

No issues.: Will not effect shellfish. Fine to eat.

Interesting question: Depends what you mean by safe. So long as the seafood is cooked to adequate temperature, there should be no increased risk of infectious disease (ie diarrhea). The other health risk involved with eating seafood involves contamination with chemicals/heavy metals. Theoretically , stirring up the sediment might increase the concentration of these contaminants, but I have found no evidence of that.

Oyster no: Any mollusks would likely have contamination after a hurricane or typhoon- mostly from storm drainage and not the stirring of the ocean floor sediment- you may have to wait for about a month after the storm is over before they are "safe" again . Crustacea like shrimp , crab,and lobster are not significantly impacted however but will need to be washed carefully. Thus prudence calls for avoidance

In the immediate: aftermath of such an event, available seafood would have already been caught. However, you're right to be concerned. Filter feeders like oysters may contain toxins from stirred up sediment. Apex predators (tuna e.g.) are more likely to accumulate heavy metals but the effect is delayed as these toxins make their way up the food chain. The long term effects of oil spills etc. are still unknown.