Where are they planted? I hope you have a huge yard as willow tree roots search out water sources like plumbing pipes, sewer pipes, etc. They are stronger than concrete! Do you happen to have a septic tank/leach field. the roots could have entered either and are showing the signs of this.
If the four trees are closest to a neighbor this could be the sign of overspray. Did the neighbor use any Roundup lately.
Have you checked the leaves for any pests? Any borers creating holes in the trunk?
Why spray with soapy water until you know what it is causing the problem? Take a sample of the leaves to the county extension office and have them determine what is going on before you treat the trees with anything.