As Elendil says, for long storage, you can just freeze as-is, in a plastic bag or other container.
As for refrigeration, there are all sorts of guidelines for various fruits, and other questions here have covered storage recommendations for specific types of fruit.
You specifically ask about strawberries and blueberries. Never put fresh berries in water, and don't even wash them until you are ready to eat them or use them (assuming you want them to last longer).
For reputable information on strawberries, see here:
The optimum storage temperature for strawberries in the home is 32° to
36°F (0° to 2°C). The optimum humidity for storage of berries to
prevent water loss and shriveling is 90 to 95 percent. Store the
fruit in the crisper drawer of your refrigerator. Keep strawberries
packaged in closed plastic clamshell containers or place fruit in a
partially opened plastic bag to maintain high humidity. Do not wash
berries until just before eating or preserving. Washing will add
moisture and will cause the berries to spoil more rapidly.
Strawberries can only be stored for up to 7 days under optimum
conditions, and that shelf life also depends on how ripe the fruit was
when purchased or picked.
The same general recommendations apply to blueberries: keep your fridge cold (just above freezing), keep humidity high by storing in crisper drawer and in containers, don't wash until ready to use. Blueberries which are picked and cooled properly should last at least a week in the fridge, perhaps even a couple weeks if you buy them relatively freshly picked.
In general, keep the berries cold as much as possible, keep them dry, and store in high humidity. Check on a regular basis and remove any berries showing signs of rot or mold.
There are various myths about keeping berries at room temperature until they are cleaned or washed, or washing fruits in vinegar to preserve them, or whatever -- don't believe them: no scientific tests have shown them to work. Just keep the fruit cold and the humidity high by keeping them in their containers (though not in a completely sealed container: that will also cause faster rot, which is why the little holes exist in the plastic supermarket containers).