For the moment, salt will help to reduce nitrite toxicity, but at about 1 tsp. per gallon you will reach the maximum usefulness of the salting. Whether you use table salt or aquarium salt is irrelevant, they're the same thing.
This tank is not finished cycling, or if it has for one reason or another the colonies crashed and you're re-cycling.
Aeration can be useful on overstocked tanks to replenish O2, but this tank is not overstocked, O2 levels are not to blame.
The fish are dieing from nitrite poisoning and it can take time for the colonies to regenerate. Do a 50% water change and rinse out all the filter media in the bucket of old tank water. Clean the gravel and remove any decaying material from the tank.
Proceed with 2 50% water changes daily, one in the morning and one in the evening, this should take care of your nitrite levels, there really aren't that many fish in the tank - for a 70 gallon.
Unless there are nitrates in your water supply, there's no reason for them to be that high. This regimen will get the NO3 levels down as well. Nitrates are an indicator of tank pollution by fish hormones and other organic compounds which we cannot measure. 40ppm should be your upper limit target, 20ppm would be more conservative and better.