It's probably not related to oil but you should change it anyway I change mine ever 3-4k
About your problem, I had the same issue when I first got my car, would put in reverse and it wouldn't go and would flash the gear on the dash.. Turn off turn back on and would go eventually but it would "jump" into the gear, CEL would go on and off occasionally and eventually stayed so I took it in and it needed a mechatronics unit.. That didn't fix it completely I later had the whole dsg replaced under extended warranty luckily and now have perfect shifts without the jerky start after hitting stop signs which was annoying.. Has it thrown any codes? Mine usually threw a code when that happened.