And Working Well -- with everything in sync and up to date....and with the right includes.
The 1.0.2 OAK update to the Arduino IDE (updated by Board Manager) includes the Blynk Library files, version 0.3.7. The update shows a simple Blynk example sketch that provides the best choice (or at least better than the ones I was guessing and using and bricking with) #includes to use. I had separate Blynk library downloads and they were getting me messed up, wrong versions etc. I recommend deleting or at least moving any Blynk libraries EXCEPT the ones included with the DigiStump 1.0.2 Board Manager files. Updated files will presumably be included with any further Arduino IDE Board Manager updates.
My Android Blynk App 1.0.0.54 June 2, 2015 (running on a Blackberry Z10 no less) now list the Digistump Oak as a choice of boards and works a treat so far. Getting Temp, Humidity and a toggeled LED widget every 20 seconds, rather I need it or not...
Includes that no longer want to brick my Oaks:
#include <SimpleTimer.h> // from Arduino home website. Not an issue
#include <ESP8266WiFi.h> //include taken from Blynk Oak example June 3, 2016
#include <BlynkSimpleEsp8266.h> //include taken from Blynk Oak example June 3, 2016
I had tried some other Esp8266 based libraries and now know how to do a serial factory reset.
I had backed Blynk on Kickstart so have a pile of energy to use, but am looking at some of the other alternative.
(some of which are free now but look like they will not stay free forever??)
James