Creating a hash from several Java string objects

Definitely don't use plain addition due to its linearity properties, but you can modify your code just slightly to achieve very good dispersion.

public String hash(String[] values) {
  long result = 17;
  for (String v:values) result = 37*result + v.hashCode();
  return String.valueOf(result);
}

It doesn't provide a 64 bit hash, but given the title of the question it's probably worth mentioning that since Java 1.7 there is java.util.Objects#hash(Object...).