Are you using the phone app or inputing from a GPS file? Strava seems to peak and zero for me quite a bit. For example on a straight level bit of road I use for time trial practice, where I'm on power all the time, the website often shows zero, followed by a huge peak, then back to zero (repeat until the end). The only way to get correct power readings is to use a power meter. According to their support forums, they think that the AVG power reading over the length of segments and rides is within 10% true, but I have my doubts.
As an example, me and my brother rode the same segment together, we are very close in weight and height (within 3lbs), no major difference in bike weight either. He recorded by phone, I recorded by Garmin. His power came out at 385w, mine at 335w, even though we rode side by side at the same pace and finished with the same time.
I think their power calculation is way off personally.