Simple demo to show how to get a Digistump Oak to change to a Static IP. Isn't the best method, but it works.

oakStaticIp.ino

//SEMI_AUTOMATIC mode to ensure variable is available
//Probably isn't needed if you don't use Particle.variable in your code
SYSTEM_MODE(SEMI_AUTOMATIC);

#include <ESP8266WiFi.h>

char myIpString[24];
IPAddress myIp;

void setup()
{
  // initialize the digital pin as an output.
  pinMode(1, OUTPUT); //LED on Oak

  //variable visible if using CLI tool or OakTerm
  Particle.variable("ipAddress", myIpString);

  //since in semi-automatic mode, need to manually connect to particle
  Particle.connect();
  
  //publish a message so we know the sketch is running
  Particle.publish("oak/userrom/msg", "I'm alive!", PRIVATE);

  //IP stuff
  IPAddress ip(192, 168, 0, 12);
  IPAddress gateway(192, 168, 0, 1);
  IPAddress subnet(255, 255, 255, 0);

  //configure the WiFi to use the 'new' settings
  WiFi.config(ip, gateway, subnet);
}

// the loop routine runs over and over again forever:
void loop()
{
  //obtain current IP address and store in variable
  myIp = WiFi.localIP();
  sprintf(myIpString, "%d.%d.%d.%d", myIp[0], myIp[1], myIp[2], myIp[3]);

  //if you don't want to use the variable, you can publish the IP string instead
  //Particle.publish("oak/userrom/currentIP", myIpString, PRIVATE);

  //make the P1 led blink for something to do...
  for (int i = 0; i < 10; i++)
  {
    digitalWrite(1, HIGH);   // turn the LED on (HIGH is the voltage level)
    delay(500);               // wait for half a second
    digitalWrite(1, LOW);    // turn the LED off by making the voltage LOW
    delay(500);               // wait for half a second
  }
}

r2 was mainly the addition of more comments, and correcting one or two mistaken comments that hadn't been changed from the initial blink code example sketch