I don't think over watering is a problem, plants roots can be submerges in water 24/7 if they get enough oxygen. I think you may have a lack of oxygen to the roots, especially of the system is basically air tight. You'll want a source of fresh air to be able to get into the root zone.

Their may have been something introduced to your hydro system like a soil born disease as well. Most likely at least one plant was contaminated. Even when washing off the soil from roots (because the pathogens attach to the roots) it spread to all the plants once in the hydro system. Strawberry are very susceptible to soil born diseases.

The hydro shop may have something to kill the pathogens/or fungus. But I would probably just dump the nutes, flush with fresh water, dump and flush with plain water again. Then fill the reservoir with just water and use something like about 1 cup of 3% hydrogen peroxide (H202) for every 5 gallons of water. Let that run through the system on normal cycles for 24 hours. Then flush the system with just plain water again. Then mix fresh nutrients, and add about 10-20 mL (2-4 Tsp) of H2O2 every day, or every other day for at least the first week. I recently did that with my pepper plants, and they didn't seem to be harmed at all. I even flushed it with 1 cup of bleach in 10 gallons of water, and they didn't seem any worse for ware from either.

Yes the H2o2 is perfect. You could try running the water 3 times a day and see how that works.

Yes the H2o2 is perfect. You could try running the water 3 times a day and see how that works.