Jabawocky - in your original post..
This last week, while tracking a radial on a VOR, at low level (3000') we had a strong headwind around 20 knots, from the 10 oclock position, at a point in time we quickly entered a less headwind area, say 10 knots, the wind vectors all changed and our GS improved. The TAS improved also by several knots.
I think tmax was absolutely right to describe this as windshear. But you seem to be talking about something different...
???
1. Sideslip
2. Down/up draught - I saw ±7 kt in my first ever motorglider trip last month (flying level with power constant).
3. Are you sure the power setting is unchanged - how accurately can you measure that?