OK, for future reference, this is called a calculation in the PDF world, not a validation. A validation is when you want to verify that the value of a field follows a specific pattern.
Anyway, you can do it using the following code as the custom calculation script of your minimum-value field (I've also added a command to set the average field value, as you requested):
var fields = ["Field 1", "Field 2", "Field 3", "Field 4"];
var values = [];
var total = 0;
var n = 0;
for (var i in fields) {
var v = Number(this.getField(fields).valueAsString);
if (v!=0) {
values.push(v);
total+=v;
n++;
}
}
if (n==0) {
event.value = "";
this.getField("Average").value = "";
} else {
values.sort(function (a,b) {return a - b;});
event.value = values[0];
this.getField("Average").value = total/n;
}