Stamford to Peterborough is about 15 minutes, depending on where you are and the traffic. Unfortunately don’t know about Oundle but its not far.
My husband goes from Peterborough to London occasionally and hasn’t ever had a problem parking there.
Let me know if I can help further.
From (albeit limited) experience, parking at PBoro station not a challenge at that time. A large number of spaces, although cost is significant – £13 a day in the main station car park. I think there are other parking areas nearby at sub-£10 however for the daily journey.